(β ,α)−Connectivity Index of Graphs

Abstract

Let Eβ (G) be the set of paths of length β in a graph G. For an integer β ≥ 1 and a real number α, the (β,α)-connectivity index is defined as$$\begin{array}{} \displaystyle ^\beta\chi_\alpha(G)=\sum \limits_{v_1v_2 \cdot \cdot \cdot v_{\beta+1}\in E_\beta(G)}(d_{G}(v_1)d_{G}(v_2)...d_{G}(v_{\beta+1}))^{\alpha}. \end{array}$$The (2,1)-connectivity index shows good correlation with acentric factor of an octane isomers. In this paper, we compute the (2, α)-connectivity index of certain class of graphs, present the upper and lower bounds for (2, α)-connectivity index in terms of number of vertices, number of edges and minimum vertex degree and determine the extremal graphs which achieve the bounds. Further, we compute the (2, α)-connectivity index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p,q], tadpole graphs, wheel graphs and ladder graphs.

Topics on data transmission problem in software definition network

“…Let G = (V(G), E(G)) be a graph, in which V(G) and E(G) are the vertex set and the edge set, respectively. Let n = |V(G)| be the order of graph G. The standard notations and terminologies used but undefined clearly in this article can be found in Bondy and Mutry [5], Basavanagoud et al [6], Wang [7], and Gao and Wang [8]. The toughness t(G) of a graph G can be stated in the below:…”

On Computational Aspects of Bismuth Tri-Iodide

“…For details about topological indices and its applications we refer [29][30][31][32][33][34][35][36][37][38][39].…”

Useful Irregularity Indices in QSPR Study for Bismuth Tri-Iodide

“…All these irregularity indices belong to degreebased topological invariants except IRM2(G) and are used in QSAR. [45][46][47][48][49]. It can be noted that many irregularity indices are constructed with the help of many known TIs.…”