Graphs with the same CDC on 8 Vertices

Here we give an exhaustive list of all 32 pairs of non-isomorphic graphs on 8 vertices which have the same CDC. This automatically includes those graphs on ⩽ 8 vertices since any \(n\leqslant8\) vertex pair of graphs \(G\), \(H\) with the same CDC will appear here as the pair \(G+(8-n)K_1\), \(H+(8-n)K_1\). For relevant definitions, please refer to my undergraduate dissertation, or my paper on the subject with Irene Sciriha.

The numbering of the graphs here is in accordance with the graph data on Brendan McKay's webpage. The colouring of the vertices (and walk matrix rows) is so that vertices of the same colour have the same number of \(k\)-walks, for any value of \(k\).

It's easy to work with these graphs in Mathematica by importing them from McKay's webpage; the pairs of numbers are available as CSV files from the root directory of this site in the form cdcX.csv. (X here stands for the number of vertices; the graphs pairs on this webpage correspond to those in cdc8.csv). For instance:

Click on code to copy to clipboard

I have also computed the pairs for X=6, 7 and 9, you can see more about those here. Notice that I am making use of the Walks package above.

Ryser Switches

A Ryser switch is a degree-sequence preserving operation on a pair of edges in a given graph. In the list below, it turns out that all but one pair of graphs is the result of a single Ryser switch. (The exceptional pair (5358, 11716) requires two).

Given a graph \(G\) and edges \(uv, xy\in E(G)\) such that \(ux, vy\notin E(G)\), the Ryser switch on the edges \(uv\) and \(xy\) replaces those edges with \(ux\) and \(vy\). We denote the graph obtained by \(\operatorname{ryser}(G,uv,xy)\).

Pair (447, 958)

Eigenvalues

\(-1\), \(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{0}\), \(\boldsymbol{0}\), \(\boldsymbol{2}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(\boldsymbol{0}\), \(\boldsymbol{0}\), \(\boldsymbol{2}\), \(\boldsymbol{2}\)

\(\begin{pmatrix}\color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{blue}1&\color{blue}0\\ \color{blue}1&\color{blue}0\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\end{pmatrix}\)

CDC

Ryser Switch

\(G_{958}=\operatorname{ryser}(G_{447},16, 38)\)

Pair (1030, 1162)

Eigenvalues

\(-1\), \(-1\), \(\boldsymbol{0.31}\), \(\boldsymbol{0.31}\), \(\boldsymbol{-1.48}\), \(\boldsymbol{-1.48}\), \(\boldsymbol{2.17}\), \(\boldsymbol{2.17}\)

Eigenvalues

\(-0.31\), \(-1\), \(1\), \(1.48\), \(-2.17\), \(\boldsymbol{0.31}\), \(\boldsymbol{-1.48}\), \(\boldsymbol{2.17}\)

\(\begin{pmatrix}\color{red}1&\color{red}2&\color{red}5\\ \color{red}1&\color{red}2&\color{red}5\\ \color{blue}1&\color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}1&\color{blue}3\\ \color{red}1&\color{red}2&\color{red}5\\ \color{red}1&\color{red}2&\color{red}5\\ \color{green}1&\color{green}3&\color{green}5\\ \color{green}1&\color{green}3&\color{green}5\end{pmatrix}\)

CDC

Ryser Switch

\(G_{1162}=\operatorname{ryser}(G_{1030},15, 26)\)

Pair (1032, 1164)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{0}\), \(\boldsymbol{0.47}\), \(\boldsymbol{-1.81}\), \(\boldsymbol{2.34}\)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{0}\), \(\boldsymbol{0.47}\), \(\boldsymbol{-1.81}\), \(\boldsymbol{2.34}\)

\(\begin{pmatrix}\color{red}1&\color{red}2&\color{red}5&\color{red}11\\ \color{red}1&\color{red}2&\color{red}5&\color{red}11\\ \color{blue}1&\color{blue}2&\color{blue}6&\color{blue}12\\ \color{green}1&\color{green}0&\color{green}0&\color{green}0\\ \color{red}1&\color{red}2&\color{red}5&\color{red}11\\ \color{red}1&\color{red}2&\color{red}5&\color{red}11\\ \color{yellow}1&\color{yellow}3&\color{yellow}6&\color{yellow}16\\ \color{yellow}1&\color{yellow}3&\color{yellow}6&\color{yellow}16\end{pmatrix}\)

CDC

Ryser Switch

\(G_{1164}=\operatorname{ryser}(G_{1032},15, 26)\)

Pair (1105, 1235)

Eigenvalues

\(0\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{0.64}\), \(\boldsymbol{-2.32}\), \(\boldsymbol{2.68}\)

Eigenvalues

\(0\), \(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{0.64}\), \(\boldsymbol{-2.32}\), \(\boldsymbol{2.68}\)

\(\begin{pmatrix}\color{red}1&\color{red}2&\color{red}6\\ \color{red}1&\color{red}2&\color{red}6\\ \color{blue}1&\color{blue}2&\color{blue}8\\ \color{blue}1&\color{blue}2&\color{blue}8\\ \color{red}1&\color{red}2&\color{red}6\\ \color{red}1&\color{red}2&\color{red}6\\ \color{green}1&\color{green}4&\color{green}8\\ \color{green}1&\color{green}4&\color{green}8\end{pmatrix}\)

CDC

Ryser Switch

\(G_{1235}=\operatorname{ryser}(G_{1105},15, 26)\)

Pair (3392, 3494)

Eigenvalues

\(0\), \(0\), \(-1\), \(1\), \(\boldsymbol{\frac{1}{2} \left(1-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1+\sqrt{17}\right)}\), \(\frac{1}{2} \left(-1-\sqrt{17}\right)\), \(\frac{1}{2} \left(\sqrt{17}-1\right)\)

Eigenvalues

\(0\), \(0\), \(-1\), \(-1\), \(\boldsymbol{\frac{1}{2} \left(1-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1+\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1+\sqrt{17}\right)}\)

\(\begin{pmatrix}\color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\end{pmatrix}\)

CDC

Ryser Switch

\(G_{3494}=\operatorname{ryser}(G_{3392},57, 68)\)

Pair (3482, 3592)

Eigenvalues

\(-0.31\), \(-1\), \(1\), \(1.48\), \(-2.17\), \(\boldsymbol{0.14}\), \(\boldsymbol{-2.27}\), \(\boldsymbol{3.13}\)

Eigenvalues

\(0.31\), \(-1\), \(-1\), \(-1.48\), \(2.17\), \(\boldsymbol{0.14}\), \(\boldsymbol{-2.27}\), \(\boldsymbol{3.13}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}11\\ \color{blue}1&\color{blue}2&\color{blue}7\\ \color{red}1&\color{red}3&\color{red}11\\ \color{blue}1&\color{blue}2&\color{blue}7\\ \color{green}1&\color{green}3&\color{green}9\\ \color{green}1&\color{green}3&\color{green}9\\ \color{yellow}1&\color{yellow}4&\color{yellow}11\\ \color{yellow}1&\color{yellow}4&\color{yellow}11\end{pmatrix}\)

CDC

Ryser Switch

\(G_{3592}=\operatorname{ryser}(G_{3482},25, 46)\)

Pair (3413, 3779)

Eigenvalues

\(0\), \(-1\), \(-1\), \(1\), \(-2\), \(2\), \(\boldsymbol{\frac{1}{2} \left(1-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1+\sqrt{17}\right)}\)

Eigenvalues

\(0\), \(1\), \(1\), \(1\), \(-2\), \(-2\), \(\boldsymbol{\frac{1}{2} \left(1-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1+\sqrt{17}\right)}\)

\(\begin{pmatrix}\color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\end{pmatrix}\)

CDC

Ryser Switch

\(G_{3779}=\operatorname{ryser}(G_{3413},15, 48)\)

Pair (1270, 5629)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-2\), \(\boldsymbol{1}\), \(\boldsymbol{1}\), \(\boldsymbol{1}\), \(\boldsymbol{2}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(-1\), \(\boldsymbol{1}\), \(\boldsymbol{2}\), \(\boldsymbol{2}\)

\(\begin{pmatrix}\color{red}1&\color{red}1\\ \color{blue}1&\color{blue}2\\ \color{blue}1&\color{blue}2\\ \color{blue}1&\color{blue}2\\ \color{red}1&\color{red}1\\ \color{blue}1&\color{blue}2\\ \color{blue}1&\color{blue}2\\ \color{blue}1&\color{blue}2\end{pmatrix}\)

CDC

Ryser Switch

\(G_{5629}=\operatorname{ryser}(G_{1270},26, 48)\)

Pair (5684, 5718)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{1}\), \(\boldsymbol{-2}\), \(\boldsymbol{3}\)

Eigenvalues

\(-1\), \(-1\), \(\boldsymbol{1}\), \(\boldsymbol{1}\), \(\boldsymbol{1}\), \(\boldsymbol{-2}\), \(\boldsymbol{-2}\), \(\boldsymbol{3}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}11\\ \color{blue}1&\color{blue}2&\color{blue}6\\ \color{blue}1&\color{blue}2&\color{blue}6\\ \color{red}1&\color{red}3&\color{red}11\\ \color{blue}1&\color{blue}2&\color{blue}6\\ \color{blue}1&\color{blue}2&\color{blue}6\\ \color{green}1&\color{green}4&\color{green}10\\ \color{green}1&\color{green}4&\color{green}10\end{pmatrix}\)

CDC

Ryser Switch

\(G_{5718}=\operatorname{ryser}(G_{5684},25, 36)\)

Pair (3887, 5753)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(-2\), \(\boldsymbol{0}\), \(\boldsymbol{0}\), \(\boldsymbol{3}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-2\), \(2\), \(\boldsymbol{0}\), \(\boldsymbol{0}\), \(\boldsymbol{3}\)

\(\begin{pmatrix}\color{red}1&\color{red}2\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\\ \color{green}1&\color{green}0\\ \color{blue}1&\color{blue}3\\ \color{blue}1&\color{blue}3\\ \color{red}1&\color{red}2\\ \color{yellow}1&\color{yellow}4\end{pmatrix}\)

CDC

Ryser Switch

\(G_{5753}=\operatorname{ryser}(G_{3887},15, 37)\)

Pair (3899, 5755)

Eigenvalues

\(-1\), \(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{0}\), \(\boldsymbol{1-\sqrt{7}}\), \(\boldsymbol{1+\sqrt{7}}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{0}\), \(\boldsymbol{1-\sqrt{7}}\), \(\boldsymbol{1+\sqrt{7}}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}12\\ \color{red}1&\color{red}3&\color{red}12\\ \color{red}1&\color{red}3&\color{red}12\\ \color{blue}1&\color{blue}0&\color{blue}0\\ \color{red}1&\color{red}3&\color{red}12\\ \color{red}1&\color{red}3&\color{red}12\\ \color{red}1&\color{red}3&\color{red}12\\ \color{green}1&\color{green}6&\color{green}18\end{pmatrix}\)

CDC

Ryser Switch

\(G_{5755}=\operatorname{ryser}(G_{3899},15, 37)\)

Pair (3886, 5756)

Eigenvalues

\(-1\), \(1\), \(1\), \(1\), \(-2\), \(-2\), \(\boldsymbol{1-\sqrt{2}}\), \(\boldsymbol{1+\sqrt{2}}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(1\), \(-2\), \(2\), \(\boldsymbol{1-\sqrt{2}}\), \(\boldsymbol{1+\sqrt{2}}\)

\(\begin{pmatrix}\color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{blue}1&\color{blue}3\\ \color{green}1&\color{green}1\\ \color{blue}1&\color{blue}3\\ \color{red}1&\color{red}2\\ \color{red}1&\color{red}2\\ \color{blue}1&\color{blue}3\end{pmatrix}\)

CDC

Ryser Switch

\(G_{5756}=\operatorname{ryser}(G_{3886},15, 37)\)

Pair (3888, 5759)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{-0.49}\), \(\boldsymbol{0.60}\), \(\boldsymbol{-2.20}\), \(\boldsymbol{3.09}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{-0.49}\), \(\boldsymbol{0.60}\), \(\boldsymbol{-2.20}\), \(\boldsymbol{3.09}\)

\(\begin{pmatrix}\color{red}1&\color{red}2&\color{red}6&\color{red}20\\ \color{blue}1&\color{blue}3&\color{blue}10&\color{blue}29\\ \color{blue}1&\color{blue}3&\color{blue}10&\color{blue}29\\ \color{green}1&\color{green}1&\color{green}5&\color{green}13\\ \color{blue}1&\color{blue}3&\color{blue}10&\color{blue}29\\ \color{blue}1&\color{blue}3&\color{blue}10&\color{blue}29\\ \color{red}1&\color{red}2&\color{red}6&\color{red}20\\ \color{yellow}1&\color{yellow}5&\color{yellow}13&\color{yellow}45\end{pmatrix}\)

CDC

Ryser Switch

\(G_{5759}=\operatorname{ryser}(G_{3888},15, 37)\)

Pair (3903, 5761)

Eigenvalues

\(-1\), \(-1\), \(1\), \(1\), \(\boldsymbol{-2}\), \(\boldsymbol{-2}\), \(\boldsymbol{2-\sqrt{3}}\), \(\boldsymbol{2+\sqrt{3}}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{-2}\), \(\boldsymbol{2-\sqrt{3}}\), \(\boldsymbol{2+\sqrt{3}}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}13\\ \color{red}1&\color{red}3&\color{red}13\\ \color{red}1&\color{red}3&\color{red}13\\ \color{blue}1&\color{blue}1&\color{blue}7\\ \color{red}1&\color{red}3&\color{red}13\\ \color{red}1&\color{red}3&\color{red}13\\ \color{red}1&\color{red}3&\color{red}13\\ \color{green}1&\color{green}7&\color{green}19\end{pmatrix}\)

CDC

Ryser Switch

\(G_{5761}=\operatorname{ryser}(G_{3903},15, 37)\)

Pair (6471, 7012)

Eigenvalues

\(-1\), \(-1\), \(2\), \(\boldsymbol{0}\), \(\boldsymbol{0.55}\), \(\boldsymbol{-1.48}\), \(\boldsymbol{-2.29}\), \(\boldsymbol{3.21}\)

Eigenvalues

\(1\), \(1\), \(-2\), \(\boldsymbol{0}\), \(\boldsymbol{0.55}\), \(\boldsymbol{-1.48}\), \(\boldsymbol{-2.29}\), \(\boldsymbol{3.21}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}10&\color{red}32&\color{red}102\\ \color{red}1&\color{red}3&\color{red}10&\color{red}32&\color{red}102\\ \color{blue}1&\color{blue}2&\color{blue}8&\color{blue}22&\color{blue}78\\ \color{green}1&\color{green}2&\color{green}7&\color{green}21&\color{green}71\\ \color{green}1&\color{green}2&\color{green}7&\color{green}21&\color{green}71\\ \color{yellow}1&\color{yellow}4&\color{yellow}11&\color{yellow}39&\color{yellow}117\\ \color{yellow}1&\color{yellow}4&\color{yellow}11&\color{yellow}39&\color{yellow}117\\ \color{orange}1&\color{orange}4&\color{orange}14&\color{orange}42&\color{orange}142\end{pmatrix}\)

CDC

Ryser Switch

\(G_{7012}=\operatorname{ryser}(G_{6471},14, 25)\)

Pair (6479, 7013)

Eigenvalues

\(-1\), \(-1\), \(-1-\sqrt{2}\), \(2\), \(\boldsymbol{0.53}\), \(\boldsymbol{-1.34}\), \(\boldsymbol{2.81}\), \(\sqrt{2}-1\)

Eigenvalues

\(1\), \(1\), \(-1-\sqrt{2}\), \(-2\), \(\boldsymbol{0.53}\), \(\boldsymbol{-1.34}\), \(\boldsymbol{2.81}\), \(\sqrt{2}-1\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}8\\ \color{red}1&\color{red}3&\color{red}8\\ \color{blue}1&\color{blue}3&\color{blue}9\\ \color{green}1&\color{green}2&\color{green}6\\ \color{green}1&\color{green}2&\color{green}6\\ \color{red}1&\color{red}3&\color{red}8\\ \color{red}1&\color{red}3&\color{red}8\\ \color{blue}1&\color{blue}3&\color{blue}9\end{pmatrix}\)

CDC

Ryser Switch

\(G_{7013}=\operatorname{ryser}(G_{6479},14, 25)\)

Pair (6481, 7015)

Eigenvalues

\(-1\), \(-1\), \(-2\), \(2\), \(\boldsymbol{-0.28}\), \(\boldsymbol{0.56}\), \(\boldsymbol{-1.79}\), \(\boldsymbol{3.52}\)

Eigenvalues

\(1\), \(1\), \(-2\), \(-2\), \(\boldsymbol{-0.28}\), \(\boldsymbol{0.56}\), \(\boldsymbol{-1.79}\), \(\boldsymbol{3.52}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}11&\color{red}37\\ \color{red}1&\color{red}3&\color{red}11&\color{red}37\\ \color{blue}1&\color{blue}3&\color{blue}13&\color{blue}43\\ \color{green}1&\color{green}2&\color{green}7&\color{green}24\\ \color{green}1&\color{green}2&\color{green}7&\color{green}24\\ \color{yellow}1&\color{yellow}4&\color{yellow}13&\color{yellow}48\\ \color{yellow}1&\color{yellow}4&\color{yellow}13&\color{yellow}48\\ \color{orange}1&\color{orange}5&\color{orange}17&\color{orange}61\end{pmatrix}\)

CDC

Ryser Switch

\(G_{7015}=\operatorname{ryser}(G_{6481},14, 25)\)

Pair (6476, 7026)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{1.15}\), \(\boldsymbol{-2.25}\), \(\boldsymbol{3.10}\)

Eigenvalues

\(-1\), \(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{1.15}\), \(\boldsymbol{-2.25}\), \(\boldsymbol{3.10}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}10\\ \color{red}1&\color{red}3&\color{red}10\\ \color{blue}1&\color{blue}2&\color{blue}6\\ \color{red}1&\color{red}3&\color{red}10\\ \color{red}1&\color{red}3&\color{red}10\\ \color{green}1&\color{green}3&\color{green}8\\ \color{green}1&\color{green}3&\color{green}8\\ \color{yellow}1&\color{yellow}4&\color{yellow}12\end{pmatrix}\)

CDC

Ryser Switch

\(G_{7026}=\operatorname{ryser}(G_{6476},14, 25)\)

Pair (6478, 7028)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-2\), \(2\), \(\boldsymbol{0.71}\), \(\boldsymbol{-1.49}\), \(\boldsymbol{3.78}\)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(-2\), \(\boldsymbol{0.71}\), \(\boldsymbol{-1.49}\), \(\boldsymbol{3.78}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}13\\ \color{red}1&\color{red}3&\color{red}13\\ \color{blue}1&\color{blue}2&\color{blue}8\\ \color{red}1&\color{red}3&\color{red}13\\ \color{red}1&\color{red}3&\color{red}13\\ \color{green}1&\color{green}4&\color{green}14\\ \color{green}1&\color{green}4&\color{green}14\\ \color{yellow}1&\color{yellow}6&\color{yellow}20\end{pmatrix}\)

CDC

Ryser Switch

\(G_{7028}=\operatorname{ryser}(G_{6478},14, 25)\)

Pair (6486, 7035)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{-0.34}\), \(\boldsymbol{0.66}\), \(\boldsymbol{-2.68}\), \(\boldsymbol{3.36}\)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{-0.34}\), \(\boldsymbol{0.66}\), \(\boldsymbol{-2.68}\), \(\boldsymbol{3.36}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}11&\color{red}35\\ \color{red}1&\color{red}3&\color{red}11&\color{red}35\\ \color{blue}1&\color{blue}3&\color{blue}11&\color{blue}33\\ \color{red}1&\color{red}3&\color{red}11&\color{red}35\\ \color{red}1&\color{red}3&\color{red}11&\color{red}35\\ \color{green}1&\color{green}3&\color{green}9&\color{green}33\\ \color{green}1&\color{green}3&\color{green}9&\color{green}33\\ \color{yellow}1&\color{yellow}5&\color{yellow}15&\color{yellow}55\end{pmatrix}\)

CDC

Ryser Switch

\(G_{7035}=\operatorname{ryser}(G_{6486},14, 25)\)

Pair (6488, 7037)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{0.48}\), \(\boldsymbol{-1.53}\), \(\boldsymbol{-2}\), \(\boldsymbol{4.05}\)

Eigenvalues

\(-1\), \(1\), \(1\), \(\boldsymbol{0.48}\), \(\boldsymbol{-1.53}\), \(\boldsymbol{-2}\), \(\boldsymbol{-2}\), \(\boldsymbol{4.05}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}14&\color{red}53\\ \color{red}1&\color{red}3&\color{red}14&\color{red}53\\ \color{blue}1&\color{blue}3&\color{blue}15&\color{blue}55\\ \color{red}1&\color{red}3&\color{red}14&\color{red}53\\ \color{red}1&\color{red}3&\color{red}14&\color{red}53\\ \color{green}1&\color{green}4&\color{green}16&\color{green}66\\ \color{green}1&\color{green}4&\color{green}16&\color{green}66\\ \color{yellow}1&\color{yellow}7&\color{yellow}23&\color{yellow}103\end{pmatrix}\)

CDC

Ryser Switch

\(G_{7037}=\operatorname{ryser}(G_{6488},14, 25)\)

Pair (10840, 10851)

Eigenvalues

\(1\), \(1\), \(1\), \(-2\), \(-2\), \(-2\), \(\boldsymbol{\frac{1}{2} \left(3-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(3+\sqrt{17}\right)}\)

Eigenvalues

\(-1\), \(-1\), \(1\), \(-2\), \(-2\), \(2\), \(\boldsymbol{\frac{1}{2} \left(3-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(3+\sqrt{17}\right)}\)

\(\begin{pmatrix}\color{red}1&\color{red}3\\ \color{red}1&\color{red}3\\ \color{blue}1&\color{blue}4\\ \color{blue}1&\color{blue}4\\ \color{red}1&\color{red}3\\ \color{red}1&\color{red}3\\ \color{blue}1&\color{blue}4\\ \color{blue}1&\color{blue}4\end{pmatrix}\)

CDC

Ryser Switch

\(G_{10851}=\operatorname{ryser}(G_{10840},14, 36)\)

Pair (5358, 11716)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(1\), \(1\), \(1\), \(-3\), \(\boldsymbol{3}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(-1\), \(-1\), \(\boldsymbol{3}\), \(\boldsymbol{3}\)

\(\begin{pmatrix}\color{red}1\\ \color{red}1\\ \color{red}1\\ \color{red}1\\ \color{red}1\\ \color{red}1\\ \color{red}1\\ \color{red}1\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11716}=\operatorname{ryser}(G_{5358},16, 25)\)

Pair (10867, 11731)

Eigenvalues

\(0\), \(-1\), \(1\), \(-2\), \(\boldsymbol{\frac{1}{2} \left(3-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(3+\sqrt{17}\right)}\), \(\frac{1}{2} \left(-1-\sqrt{17}\right)\), \(\frac{1}{2} \left(\sqrt{17}-1\right)\)

Eigenvalues

\(0\), \(-1\), \(-1\), \(-2\), \(\boldsymbol{\frac{1}{2} \left(3-\sqrt{17}\right)}\), \(\boldsymbol{\frac{1}{2} \left(3+\sqrt{17}\right)}\), \(\frac{1}{2} \left(1-\sqrt{17}\right)\), \(\frac{1}{2} \left(1+\sqrt{17}\right)\)

\(\begin{pmatrix}\color{red}1&\color{red}3\\ \color{red}1&\color{red}3\\ \color{blue}1&\color{blue}4\\ \color{blue}1&\color{blue}4\\ \color{red}1&\color{red}3\\ \color{red}1&\color{red}3\\ \color{blue}1&\color{blue}4\\ \color{blue}1&\color{blue}4\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11731}=\operatorname{ryser}(G_{10867},15, 26)\)

Pair (10841, 11742)

Eigenvalues

\(1\), \(1\), \(-1-\sqrt{2}\), \(-2\), \(\boldsymbol{-0.32}\), \(\boldsymbol{-1.60}\), \(\boldsymbol{3.92}\), \(\sqrt{2}-1\)

Eigenvalues

\(-1\), \(-1\), \(-1-\sqrt{2}\), \(2\), \(\boldsymbol{-0.32}\), \(\boldsymbol{-1.60}\), \(\boldsymbol{3.92}\), \(\sqrt{2}-1\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}12\\ \color{red}1&\color{red}3&\color{red}12\\ \color{blue}1&\color{blue}4&\color{blue}16\\ \color{blue}1&\color{blue}4&\color{blue}16\\ \color{red}1&\color{red}3&\color{red}12\\ \color{red}1&\color{red}3&\color{red}12\\ \color{green}1&\color{green}5&\color{green}19\\ \color{green}1&\color{green}5&\color{green}19\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11742}=\operatorname{ryser}(G_{10841},14, 36)\)

Pair (10838, 11747)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{0}\), \(\boldsymbol{0}\), \(\boldsymbol{\frac{1}{2} \left(1-\sqrt{41}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1+\sqrt{41}\right)}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{0}\), \(\boldsymbol{0}\), \(\boldsymbol{\frac{1}{2} \left(1-\sqrt{41}\right)}\), \(\boldsymbol{\frac{1}{2} \left(1+\sqrt{41}\right)}\)

\(\begin{pmatrix}\color{red}1&\color{red}2&\color{red}8\\ \color{blue}1&\color{blue}4&\color{blue}14\\ \color{blue}1&\color{blue}4&\color{blue}14\\ \color{blue}1&\color{blue}4&\color{blue}14\\ \color{blue}1&\color{blue}4&\color{blue}14\\ \color{red}1&\color{red}2&\color{red}8\\ \color{green}1&\color{green}4&\color{green}16\\ \color{green}1&\color{green}4&\color{green}16\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11747}=\operatorname{ryser}(G_{10838},14, 36)\)

Pair (10839, 11748)

Eigenvalues

\(-1\), \(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{0.21}\), \(\boldsymbol{-2.30}\), \(\boldsymbol{4.08}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{0.21}\), \(\boldsymbol{-2.30}\), \(\boldsymbol{4.08}\)

\(\begin{pmatrix}\color{red}1&\color{red}2&\color{red}8\\ \color{blue}1&\color{blue}4&\color{blue}16\\ \color{blue}1&\color{blue}4&\color{blue}16\\ \color{blue}1&\color{blue}4&\color{blue}16\\ \color{blue}1&\color{blue}4&\color{blue}16\\ \color{red}1&\color{red}2&\color{red}8\\ \color{green}1&\color{green}5&\color{green}21\\ \color{green}1&\color{green}5&\color{green}21\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11748}=\operatorname{ryser}(G_{10839},14, 36)\)

Pair (10849, 11751)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{0.60}\), \(\boldsymbol{-1.35}\), \(\boldsymbol{-2.39}\), \(\boldsymbol{4.14}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{0.60}\), \(\boldsymbol{-1.35}\), \(\boldsymbol{-2.39}\), \(\boldsymbol{4.14}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}14&\color{red}56\\ \color{blue}1&\color{blue}4&\color{blue}17&\color{blue}69\\ \color{blue}1&\color{blue}4&\color{blue}17&\color{blue}69\\ \color{blue}1&\color{blue}4&\color{blue}17&\color{blue}69\\ \color{blue}1&\color{blue}4&\color{blue}17&\color{blue}69\\ \color{red}1&\color{red}3&\color{red}14&\color{red}56\\ \color{green}1&\color{green}4&\color{green}16&\color{green}68\\ \color{yellow}1&\color{yellow}6&\color{yellow}22&\color{yellow}96\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11751}=\operatorname{ryser}(G_{10849},14, 36)\)

Pair (10850, 11752)

Eigenvalues

\(-1\), \(1\), \(1\), \(-2\), \(-2\), \(\boldsymbol{0.14}\), \(\boldsymbol{-1.64}\), \(\boldsymbol{4.50}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-2\), \(2\), \(\boldsymbol{0.14}\), \(\boldsymbol{-1.64}\), \(\boldsymbol{4.50}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}15\\ \color{blue}1&\color{blue}4&\color{blue}19\\ \color{blue}1&\color{blue}4&\color{blue}19\\ \color{blue}1&\color{blue}4&\color{blue}19\\ \color{blue}1&\color{blue}4&\color{blue}19\\ \color{red}1&\color{red}3&\color{red}15\\ \color{green}1&\color{green}5&\color{green}23\\ \color{yellow}1&\color{yellow}7&\color{yellow}27\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11752}=\operatorname{ryser}(G_{10850},14, 36)\)

Pair (10887, 11755)

Eigenvalues

\(-0.31\), \(-1\), \(1\), \(1.48\), \(-2.17\), \(\boldsymbol{-0.72}\), \(\boldsymbol{-2.38}\), \(\boldsymbol{4.10}\)

Eigenvalues

\(0.31\), \(-1\), \(-1\), \(-1.48\), \(2.17\), \(\boldsymbol{-0.72}\), \(\boldsymbol{-2.38}\), \(\boldsymbol{4.10}\)

\(\begin{pmatrix}\color{red}1&\color{red}3&\color{red}13\\ \color{blue}1&\color{blue}4&\color{blue}17\\ \color{blue}1&\color{blue}4&\color{blue}17\\ \color{blue}1&\color{blue}4&\color{blue}17\\ \color{blue}1&\color{blue}4&\color{blue}17\\ \color{red}1&\color{red}3&\color{red}13\\ \color{green}1&\color{green}5&\color{green}19\\ \color{green}1&\color{green}5&\color{green}19\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11755}=\operatorname{ryser}(G_{10887},14, 36)\)

Pair (10897, 11761)

Eigenvalues

\(0\), \(-1\), \(-1\), \(1\), \(1\), \(-2\), \(\boldsymbol{1-\sqrt{13}}\), \(\boldsymbol{1+\sqrt{13}}\)

Eigenvalues

\(0\), \(-1\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{1-\sqrt{13}}\), \(\boldsymbol{1+\sqrt{13}}\)

\(\begin{pmatrix}\color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{blue}1&\color{blue}6\\ \color{blue}1&\color{blue}6\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11761}=\operatorname{ryser}(G_{10897},14, 36)\)

Pair (10898, 11762)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(1\), \(1\), \(\boldsymbol{-2}\), \(\boldsymbol{-2}\), \(\boldsymbol{5}\)

Eigenvalues

\(-1\), \(-1\), \(-1\), \(-1\), \(-1\), \(2\), \(\boldsymbol{-2}\), \(\boldsymbol{5}\)

\(\begin{pmatrix}\color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{red}1&\color{red}4\\ \color{blue}1&\color{blue}7\\ \color{blue}1&\color{blue}7\end{pmatrix}\)

CDC

Ryser Switch

\(G_{11762}=\operatorname{ryser}(G_{10898},14, 36)\)

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