Graphs with at most Four Seidel Eigenvalues
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Authors: M. GHORBANI, M. HAKIMI-NEZHAAD AND B. ZHOU
DOI: 10.46793/KgJMat2302.173G
Abstract:
Let G be a graph of order n with adjacency matrix A(G). The eigenvalues of matrix S(G) = Jn − In − 2A(G), where Jn is the n by n matrix with all entries 1, are called the Seidel eigenvalues of G. Let ????(n,r) be the set of all graphs of order n with a single Seidel eigenvalue with multiplicity r. In the present work, we will characterize all graphs in the class ????(n,n − i) for i = 1, 2 and for the case i = 3 our characterization is done by this condition that the nullity of S(G) is zero. If the nullity of S(G) is not zero the problem is solved in special cases.
Keywords:
Interlacing theorem, Seidel eigenvalue, Seidel switching, nullity.
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