Graph Indices for Cartesian Product of -sum of Connected Graphs.

BACKGROUND: A topological index is a real number associated with a graph that provides information about its physical and chemical properties and their correlations. Topological indices are being used successfully in Chemistry, Computer Science, and many other fields. METHODS: In this article, we apply the well-known Cartesian product on F-sums of connected and finite graphs. We formulate sharp limits for some famous degree-dependent indices. RESULTS: Zagreb indices for the graph operations T(G), Q(G), S(G), R(G), and their F-sums have been computed. By using orders and sizes of component graphs, we derive bounds for Zagreb indices, F-index, and Narumi-Katayana index. CONCLUSION: The formulation of expressions for the complicated products on F-sums, in terms of simple parameters like maximum and minimum degrees of basic graphs, reduces the computational complexities.

On the bounds of degree-based topological indices of the Cartesian product of F-sum of connected graphs.

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, Randic 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.