Eigenvalues of the adjacency matrix for the 10-node Petersen graph.
-2, -2, -2, -2, 1, 1, 1, 1, 1, 3
1
There are 30240 adjacency matrices for this graph, but they all have the same set of eigenvalues.
T. D. Noe, Plot of 10 terms
Eric W. Weisstein, MathWorld: Petersen Graph
(Mma) t = Table[0, {10}, {10}]; con = {{2, 5, 6}, {1, 3, 7}, {2, 4, 8}, {3, 5, 9}, {1, 4, 10}, {1, 8, 9}, {2, 9, 10}, {3, 6, 10}, {4, 6, 7}, {5, 7, 8}}; Do[t[[i, con[[i]]]] = t[[con[[i]], i]] = 1, {i, 10}]; Sort[Eigenvalues[t]]
Cf. S000392.
nonn,full
T. D. Noe, Dec 08 2014