## S000392

An adjacency matrix for the 10-node Petersen graph.

0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0

1

The eigenvalues of this matrix are 3, 1, 1, 1, 1, 1, -2, -2, -2, -2. This graph has exactly 30240 = 6*7! similar adjacency matrices. This matrix is formed from the top left diagram in Weissteins webpage; label the outer circle of points 1 to 5 and the inner circle of points 6 to 10, both clockwise from the top.

T. D. Noe, Plot of 100 terms

Eric W. Weisstein, MathWorld: Petersen Graph

Matrix:
0, 1, 0, 0, 1, 1, 0, 0, 0, 0
1, 0, 1, 0, 0, 1, 1, 0, 0, 0
0, 1, 0, 1, 0, 0, 0, 1, 0, 0
0, 0, 1, 0, 1, 0, 0, 0, 1, 0
1, 0, 0, 1, 0, 0, 0, 0, 0, 1
1, 1, 0, 0, 0, 0, 0, 1, 1, 0
0, 1, 0, 0, 0, 0, 0, 0, 1, 1
0, 0, 1, 0, 0, 1, 0, 0, 0, 1
0, 0, 0, 1, 0, 1, 1, 0, 0, 0
0, 0, 0, 0, 1, 0, 1, 1, 0, 0

(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}]; MatrixForm[t]

Cf. S000393.

nonn,full

T. D. Noe, Dec 05 2014