8 research outputs found
The graphs with all but two eigenvalues equal to or
We determine all graphs for which the adjacency matrix has at most two
eigenvalues (multiplicities included) not equal to , or , and determine
which of these graphs are determined by their adjacency spectrum
Notes on simplicial rook graphs
The simplicial rook graph is the graph of which the vertices
are the sequences of nonnegative integers of length summing to , where
two such sequences are adjacent when they differ in precisely two places. We
show that has integral eigenvalues, and smallest eigenvalue , and that this graph has a large part of its
spectrum in common with the Johnson graph . We determine the
automorphism group and several other properties
The graphs with all but two eigenvalues equal to - 2 or 0
We determine all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from and decide which of these graphs are determined by their spectrum. This includes the so-called friendship graphs, which consist of a number of edge-disjoint triangles meeting in one vertex. It turns out that the friendship graph is determined by its spectrum, except when the number of triangles equals sixteen