Bounds on Path Energy of Graphs

Published 10 May 2022 in math.CO and cs.DM | (2205.05100v4)

Abstract: Given a graph $M,$ path eigenvalues are eigenvalues of its path matrix. The path energy of a simple graph $M$ is equal to the sum of the absolute values of the path eigenvalues of the graph $M$ (Shikare et. al, 2018). We have discovered new upper constraints on path energy in this study, expressed in terms of a graph's maximum degree. Additionally, a relationship between a graph's energy and path energy is given.

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