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.
