ABSTRACT: For two vertices v_j and v_k of a graph G, the usual distance D_jk, is the length of the shortest path between vertices v_j and v_k. In this paper, we introduce a new concept named D^d Distance energy by considering the degrees of various vertices presented in the path, in addition to the length of the path for j≠k and zero otherwise. Also, we compute the D^d Distance energy of some standard graphs.


KEYWORDS: D^d Distance, D^d Distance matrix, D^d Distance energy, Cocktail party graph, Crown graph, Friendship graph.
2020 Mathematics Subject Classification: 05C50, 05C12.