On P(k) path eigenvalues and P(k) path energy of graphs.

Given a graph G with vertex set V (G) = { v 1 , v 2 , ... , v n } , we associate to it a P (k) path matrix whose (i , j) entry represents the maximum number of vertex disjoint path with the length k from v i to v j for i ≠ j and P i j (k) = 0 if i = j. The eigenvalues of this matrix are called the path eigenvalues of the graph. In this note, we investigate P (k) path energy of some classes of graphs and several results concerning P (k) path energy has been obtained. [ABSTRACT FROM AUTHOR]