Distance spectra of some graph operations and some new distance equienergetic graphs of diameter 3

Abstract

Two graphs of same order are said to be distance equienergetic if their distance energies are same. In this paper, we first give a partial insight on the distance spectrum of Mycielskian graphs and then we focus on constructing distance equienergetic graphs by introducing three new graph operations. As an application of our results, we construct some new class of distance equinergetic graphs of diameter 3 on 18+2n vertices for all n ≥ 1.