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Title:
On Bounds of Energy of a Graph with Self-Loops
Authors:
Abujafar Mandal, Shaikh Mohammed Abu Nayeem
doi:
Volume
92
Issue
3
Year
2024
Pages
703-727
Abstract

The energy of a graph GS with n vertices and σ self-loops is defined as ε(GS)=i=1n|λiσn|, where the eigenvalues of the adjacency matrix of GS are λ1,λ2,,λn. In this article, we have established some upper and lower bounds for the energy of such a graph. Those new bounds involve parameters like number of vertices (n), number of edges (m), number of self-loops (σ), maximum vertex degree (Δ), and minimum vertex degree (δ). We show that for 1σ<n, the quantity |λiσn| is always greater than 0, and using that fact we establish a lower bound. We have compared and concluded that the new bounds are either better than the existing bounds or incomparable to a few bounds obtained by some researchers recently.

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