On diameter and distance energy of complement of regular graphs

In this paper, we investigate the diameter and distance energy of the complement of a regular graph G. We improve and extend earlier results on the diameter and distance energy of graph complements obtained by Indulal [Algebr. Struct. Appl. ۴ (۲۰۱۷) ۵۳-۵۸], removing the restrictions on the relationship between the degree r and the order n of the graph. We also derive a formula for the distance energy of the complement of a regular graph in terms of its adjacency energy and eigenvalues. This formula facilitates the characterization and construction of families of distance equienergetic graphs from adjacency equienergetic ones. Furthermore, we enhance some findings related to an open problem concerning adjacency and distance equienergetic graphs.

کلیدواژه ها:

Diameter of a graph ، Distance energy ، Distance equienergetic graphs ، Equienergetic graphs ، Graph energy ، Iterated line graphs