Graphs and Degree Equitability

Abstract

<p> Let G=(<em>V,E</em>) be a graph. If <em>φ</em> is a function from the vertex set <em>V(G)</em> to the set of positive integers. Then two vertices u, v ∈ <em>V</em>(<em>G</em>) are φ -equitable if｜<em>φ</em>(u)－<em>φ</em>(v)｜≤1.By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained. </p> <p> <br /> </p

QSPR Analysis of Polycyclic Aromatic Hydrocarbons

“…The values for the respective physico-chemical properties, were acquired from ChemSpider as shown in Table (2). Table (1) enlists the calculated equitable and non-equitable degree-based topological indices of related molecular graphs. The correlation coefficient (r) values for the characteristics are expressed with specified equitable and non-equitable topological index in the Table (3).…”