INCIDENCE ENERGY OF SUBGRAPH COMPLEMENTS OF GRAPHS

Incidence energy of the graph G, denoted by IE(G), is defined as the sum of the singular values of its incidence matrix. The notion of incidence energy of subgraph complements of a graph has been proposed in this study. The expression for the sum of singular values and eigenvalues of [I(G ⊕ S)] and [I(G ⊕ S)][I(G ⊕ S)]^T, respectively has been obtained. Additionally, we have noted the changes in the trace of [I(G ⊕ S)][I(G ⊕ S)]^T upon deleting an edge of G ⊕ S. We have characterized incidence energy of subgraph complement of P_n and K_{1, n−1} and also, obtained some bounds for incidence energy of subgraph complements of a graph. The incidence energy of subgraph complement of complete graph, complete bipartite graph and star has been computed.