Mathematic Properties and their Chemical Applicabilities of Atom Valency Block Indices

The Atom Valency Block (AVB) Indices of an undirected, finite, simple, connected molecular graph/graph G = (V, E) are defined as〖 AVB〗_1 (G) ∑_(u∈V)▒〖[d(u)b(u)] 〗and〖 AVB〗_2 (G)=∑_(u∈V)▒〖[d(u)×b(u)]〗, where the valency (or degree) d(u) of an atom (or vertex) u is the number of atoms adjacent to u, and the block number b(u) of an atom (vertex) u represents the number of blocks of G containing u (the maximal non-separable subgraph of a graph is said to be the block of that graph). In this article, we initiate these new molecular descriptors to compute exact values of separable and non-separable graph and found some inequalities in terms of the order, size, and minimum/maximum valency. Also, we have made comparisons concerning other pre-existing atom valency-based descriptors. In addition, we present the statistical analysis of some chemical trees via scatter plotted correlations between AVB indices and other well-known atom valency-based descriptors.