On equipathenergetic graphs and new bounds on path energy

05/10/2022

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by   Amol P. Narke, et al.

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The path eigenvalues of a graph G are the eigenvalues of its path matrix. The path energy of a simple connected graph G is equal to the sum of the absolute values of the path eigenvalues of the graph G (Shikare et. al, 2018). In this paper we define equipathenergetic and n-equipathenergetic graphs. We study their properties and several ways to construct the equipathenergetic and n-equipathenergetic graphs. We have found new upper bounds on path energy in terms of the maximum degree of a graph. A relation between energy and path energy of a graph is also provided.