Seidel borderenergetic graphs

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 n-ary union 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 ?= where n is even. Finally, we determine all Seidel borderenergetic graphs with at most 10 vertices.