The effect of graph operations on the degree-based entropy

The degree-based entropy I-d(G ) of a graph G on m > 0 edges is obtained from the well-known Shannon entropy - sigma(n)(i=1)p(x(i)) logp(x(i)) in information theory by replacing the probabilities p(x(i)) by the fractions d(G)(v(i))/2m , where { v(1), v(2), ..., v(n)} is the vertex set of G , and d(G)(v(i)) is the degree of v(i). We continue earlier work on I-d(G ) . Our main results deal with the effect of a number of graph operations on the value of I-d(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. (C) 2022 The Authors. Published by Elsevier Inc.