Variable Sum Exdeg Energy of Graphs

Abstract

In mathematical chemistry, a topological index of a graph is a molecular descriptor which is obtained for a chemical compound from its molecular graph. This graph invariant is a numerical parameter used to characterize the graph topology. The study of energy of a graph was introduced in 1978 by Gutman. Recently, the study on topological indices has gained a lot of signi cance and is extensively studied concept in spectral graph theory. Variable Sum exdeg index SEIv is the graph property rst studied by Vuki cevi c. The author studied the extremal graphs among di erent classes with respect to SEIv for v >1 and the polynomial form of this graph is also introduced. In this thesis the concept of variable sum exdeg energy of graphs is established. The algebraic properties of variable sum exdeg energy of a graph are studied. Some properties related to spectral radius of variable sum exdeg matrix are determined. Nordhaus-Gaddum type results for variable sum exdeg energy and spectral radius are given. Some classes of variable sum exdeg equienergetic graphs are also obtained.