SEIDEL BORDERENERGETIC GRAPHS

Year 2020, Volume: 10 Issue: 2, 389 - 399, 01.03.2020

M. H. Nezhaad M. Ghorbani

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 ∼= K n 2 , n 2 where n is even. Finally, we determine all Seidel borderenergetic graphs with at most 10 vertices.

Keywords

Seidel matrix, Seidel eigenvalue, Seidel borderenergetic graph

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