Distance energy of partial complementary graph

Abstract

The partial complement of a graph G with respect to a set S is the graph obtained from G by removing the edges of induced subgraph 〈S〉 and adding edges which are not in 〈S〉 of G. In this paper we introduce the concept of distance energy of connected partial complements of a graph. Few properties on distance eigenvalues and bounds for distance energy of connected partial complement of a graph are achieved. Further distance energy of connected partial complement of some families of graphs are computed.