Relations between ordinary energy and energy of a self-loop graph

Document Type

Article

Publication Title

Heliyon

Abstract

Let G be a graph on n vertices with vertex set V(G) and let S⊆V(G) with |S|=α. Denote by GS, the graph obtained from G by adding a self-loop at each of the vertices in S. In this note, we first give an upper bound and a lower bound for the energy of GS (E(GS)) in terms of ordinary energy (E(G)), order (n) and number of self-loops (α). Recently, it is proved that for a bipartite graph GS, E(GS)≥E(G). Here we show that this inequality is strict for an unbalanced bipartite graph GS with 0<α

DOI

10.1016/j.heliyon.2024.e27756

Publication Date

3-30-2024

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