Abstract
Motivated by the concept of Shannon’s entropy, the degree-dependent weighted graph entropy was defined which is now become a tool for measurement of structural information of complex graph networks. The aim of this paper is to study weighted graph entropy. We used GA and Gaurava indices as edge weights to define weighted graph entropy and establish some bounds for different families of graphs. Moreover, we compute the defined weighted entropies for molecular graphs of some dendrimer structures.
Highlights
Ere are many interesting attributes on topological indices, and different physicochemical properties of hydrocarbons can be obtained from this index [11,12,13,14,15,16]. e predictive power of the GA index is compared with others such as the famous Randicindex [17]
We always consider G being a connected graph with E as the set of edges, V as the set of vertices, and w to be the edge weight given to the edges of graph G that will be used to define weighted graph entropy
The graph entropy is a measure of the information rate achievable by communicating symbols over a channel in which certain pairs of values may be confused. is measure, first introduced by Korner in the 1970s, has since proven itself useful in other settings, including combinatorics
Summary
Ere are many interesting attributes on topological indices, and different physicochemical properties of hydrocarbons can be obtained from this index [11,12,13,14,15,16]. e predictive power of the GA index is compared with others such as the famous Randicindex [17]. Different molecular descriptors are used to introduce weighted graph entropies [28,29,30,31]. We extended the work of [28, 30] and introduced weighted graph entropies by using GA and Gaurava indices as edge weights. The weighted graph entropy can be defined by
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