SEIDEL BORDERENERGETIC GRAPHS

SEIDEL BORDERENERGETIC GRAPHS

M. H. Nezhaad, M. Ghorbani

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Abstract

A graph G of order n is said to be Seidel borderenergetic if its Seidel energy equals the Seidel energy of the complete graph Kn. Let G be graph on n vertices with two distinct Seidel eigenvalues. In this paper, we prove that G is Seidel borderenergetic if and only if G = Kn or G = Kn or G = Ki [ Kj or G = Ki;j , where i + j = n. We also, show that if G is a connected k-regular graph on n  3 vertices with three distinct eigenvalues, then G is Seidel borderenergetic if and only if G = Kn2;n2 where n is even. Finally, we determine all Seidel borderenergetic graphs with at most 10 vertices.

Keywords

Seidel matrix, Seidel eigenvalue, Seidel borderenergetic graph.