SPECTRUM AND ENERGY OF THE TRANSFORMATION GRAPH KN++

Abstract: Let G be a graph. The eigen values of G are the eigen values obtained from the adjacency matrix of G. The energy of a graph G denoted by E(G), is the sum of absolute values of its eigen values. One of the questions that arises here is, Is it possible to find the energy of graph by graph transformation? This paper answers this question. Here a category of graph called complete graph is taken and is operated to obtain transformation graph . It has been proved that the spectrum and energy of this transformation graph is -1 with multiplicity (n+2)(n-1)/2 and (n+2)(n-1)/2 and its energy is (n+2)(n-1).

Keywords: Energy, complete graph, transformation graph, Kn++-