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 − ∑ i = 1 n p (x i) log p (x i) in information theory by replacing the probabilities p (x i) by the fractions d G (v i) 2 m , 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. [ABSTRACT FROM AUTHOR]