Reciprocal distance energy of complete multipartite graphs

Abstract

In this paper, first we compute the energy of a special partitioned matrix under some cases. As a consequence, we obtain the reciprocal distance energy of the complete multipartite graph and also we give various other energies of complete multipartite graphs. Next, we show that among all complete [Formula: see text]-partite graphs on [Formula: see text] vertices, the complete split graph [Formula: see text] has minimum reciprocal distance energy and the reciprocal distance energy is maximum for the Turan graph [Formula: see text]. At last, it is shown that the reciprocal distance energy of the complete bipartite graph [Formula: see text] decreases under deletion of an edge if [Formula: see text], and increases if [Formula: see text]. Also, we show that the reciprocal distance energy of the complete tripartite graph does not increase under edge deletion.