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

B. R. Rakshith, Kinkar Chandra Das*, B. J. Manjunatha, Yilun Shang

*Corresponding author for this work

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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<n. In other words, we show that there exits no unbalanced bipartite graph GS with 0<α<n and E(GS)=E(G).

Original languageEnglish
Article numbere27756
Number of pages5
Issue number6
Early online date8 Mar 2024
Publication statusPublished - 30 Mar 2024

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