Minimal Degree-Based Graph Entropy for Dense Graphs
Jingzhi Yan, Guan Feng · match Communications in Mathematical and in Computer Chemistry · 2025
Various graph entropy measures derived from classical Shannon entropy are introduced to characterize the complexity of networks, among which the degree-based graph entropy is defined by employing degrees of vertices as a graph invariant. Using graph operations to explore the properties of the extremal graphs has been demonstrated a promising method. In this paper, we give conditions for decreasing the values of the entropy by graph operations, which extend and improve some known results. As an application, we characterize graphs attaining the minimum values in some connected dense graphs with given numbers of vertices and edges.