On equipathenergetic graphs and new bounds on path energy

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 . (S. Shikare et. al, 2018), where the path eigenvalues of a graph G is the path eigenvalues of its path matrix. In this paper we define equipathenergetic and n -equipathenergetic graphs, their properties and several ways to construct the equipathenergetic and n -equipathenergetic graphs. We have found new upper bounds for path energy in terms of the maximum degree of a graph. A relation between energy of a graph and path energy of a graph is also provided.