The effect of graph operations on the degree-based entropy

Abstract

The degree-based entropy Id(G) of a graph G on m>0 edges is obtained from the well-known Shannon entropy −∑i=1np(xi)logp(xi) in information theory by replacing the probabilities p(xi) by the fractions dG(vi)2m, where {v1,v2,…,vn} is the vertex set of G, and dG(vi) is the degree of vi. We continue earlier work on Id(G). Our main results deal with the effect of a number of graph operations on the value of Id(G). We also illustrate the relevance of these results by applying some of these operations to prove a number of extremal results for the degree-based entropy of trees and unicyclic graphs.