On equipathenergetic graphs and new bounds on path energy

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.