Let G be a graph with vertex set  We define a matrix whose th entry is the maximum number of vertex disjoint paths between the corresponding vertices if they are adjacent and zero otherwise. We call this matrix as path matrix of G and its eigenvalues as path eigenvalues of G. In this paper, we investigate path eigenvalues of some specific classes of graphs. The nature of largest path eigenvalues and relation between chromatic number and largest path eigenvalue have been explored.

path, spanning subgraphs, real symmetric matrix, eigenvalues, line graph.