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 <Si> and adding edges which are not in <Si> 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.