On Sensitivity of Hamming Energy of a Graph

Authors: Izudin Redžepović, Nemanja Vučićević, Nenad Stojanović

Keywords: Hamming matrix, eigenvalues, graph spectrum, graph energy, degeneracy of graph quantity

DOI: 10.46793/SPSUNP2402.159R

Abstract:

A novel graph quantity, named Hamming energy of a graph HE(G), has been proposed. It is defined as a sum of the absolute values of the eigenvalues of the Hamming matrix. To be used in chemistry, graph quantity should be able to discriminate between different isomers, i.e., it should be sensitive. Therefore, in this paper, we investigate the sensitivity of HE(G), using different sets of isomers. It was found that HE(G) shows exceptional sensitivity compared to graph energy and other eigenvalue-based graph quantities.