The Entropy of Weighted Graphs with Atomic Bond Connectivity Edge Weights

Abstract

The aim of this report to solve the open problem suggested by Chen et al. We study the graph entropy with ABC edge weights and present bounds of it for connected graphs, regular graphs, complete bipartite graphs, chemical graphs, tree, unicyclic graphs, and star graphs. Moreover, we compute the graph entropy for some families of dendrimers.

Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights

“…Weighted entropy additionally discovered applications in the coding theory [47]. In this paper, we have studied weighted entropy with augmented Zagreb edge weights, which was an open problem [35].…”

“…Degree-based topological indices correlate the structure of the molecular compound with its various physical properties, biological activities, and chemical reactivity [39]. Recently, different topological indices have been used to establish weighted graph entropies [34,35]. Research indicates that the augmented Zagreb index (AZI) possesses the best correlating ability among several topological indices [40].…”

“…In [25], Kwun et al established the weighted entropy with atomic bound connectivity edge weights. Our point is to take care of the issue proposed by Chen et al in [34] and Kwun et al in [35]. e paper is organized as follows: in Section 2, we give brief introduction about topological indices; in Section 3, we introduce weighted graph entropy with augmented Zagreb edge weights.…”

“…For instance, it gives an equal definition to a graph to be flawless, and it can likewise be connected to acquire lower bounds in graph covering problems. e objective of this study is to solve the open problem suggested by Kwun et al in 2018. In this paper, we study the weighted graph entropy by taking augmented Zagreb edge weight and give bounds of it for regular, connected, bipartite, chemical, unicyclic, etc., graphs. Moreover, we compute the weighted graph entropy of certain nanotubes and plot our results to see dependence of weighted entropy on involved parameters.…”

Some New Bounds of Weighted Graph Entropies with GA and Gaurava Indices Edge Weights

“…Many problems of information theory, biology, computer sciences, chemistry, and discrete mathematics are directly solved by utilizing different kinds of graph measures and the graph entropy is one of the powerful tools [22][23][24][25][26] that help to understand the structural complexity of graph networks [27]. Different molecular descriptors are used to introduce weighted graph entropies [28][29][30][31].…”