Abstract
Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-chemical properties and topological indices such as Zagreb, Randić and multiple Zagreb indices. In this paper, we determine the lower and upper bounds of Zagreb indices, the atom-bond connectivity (ABC) index, multiple Zagreb indices, the geometric-arithmetic (GA) index, the forgotten topological index and the Narumi-Katayama index for the Cartesian product of F-sum of connected graphs by using combinatorial inequalities.
Highlights
Introduction and preliminary results We considerG as a simple, connected and finite graph with a vertex set V (G) = {u1, u2, u3, . . . , un}, an edge set E(G) = {e1, e2, e3, . . . , em}, the order of G = |V (G)| = n and the size of G = |E(G)| = m
The number of edges having u as an end vertex is called the degree of u in G and is denoted by degG(u)
The branch of mathematical chemistry which applies graph theory to mathematical modeling of chemical phenomena is known as chemical graph theory [2]
Summary
2 Main results and discussions This section is meant for determination of bounds for the first Zagreb, the third Zagreb, the augmented Zagreb, the first multiple Zagreb, ABC and GA indices of the Cartesian product of F-sum of graphs in terms of their factor graphs.
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