Further study of eccentricity based indices for benzenoid hourglass network

Abstract

Topological Indices are the mathematical estimate related to atomic graph that corresponds biological structure with several real properties and chemical activities. These indices are invariant of graph under graph isomorphism. If top(h1) and top(h2) denotes topological index h1 and h2 respectively then h1 approximately equal h2 which implies that top(h1) = top(h2). In biochemistry, chemical science, nano-medicine, biotechnology and many other science's distance based and eccentricity-connectivity(EC) based topological invariants of a network are beneficial in the study of structure-property relationships and structure-activity relationships. These indices help the chemist and pharmacist to overcome the shortage of laboratory and equipment. In this paper we calculate the formulas of eccentricity-connectivity descriptor(ECD) and their related polynomials, total eccentricity-connectivity(TEC) polynomial, augmented eccentricity-connectivity(AEC) descriptor and further the modified eccentricity-connectivity(MEC) descriptor with their related polynomials for hourglass benzenoid network.