ON MARKER SET DISTANCE EIGENVALUES IN GRAPHS
Let be a simple undirected connected graph and let M be a non-empty subset of vertices of G. We define the M-set distance between two vertices and of G as where and denotes the usual distance between vertices u and v in G. Then the matrix is called the M-set distance matrix of the marker set M in G. Corresponding characteristic polynomial is definedas the roots of the characteristic polynomial are arranged in non-increasing order, called the M-set distance eigenvalues in G. The M-set distance spectrum and M-set energy are defined analogous to adjacency/distance spectrum and energy. In this paper, we study some preliminary results on the above defined concepts as well as their impact on other graph parameters.
marker set of a graph, M-set distance matrix, eigenvalues, distance marker set energy.