Characterizing Generalized Windmill Graphs in terms of Complexity Measures via Eccentricity Dependent Topological Indices

Windmill graphs have a crucial role in the field of computer science, mathematics, electrical engineering and physics. Generalized windmill graphs are a generalization of the classic windmill graphs with applications in network communication, optimization, wireless sensor networks, ad-hoc networks, and distributed computing systems. By studying the entropy and complexity measures of generalized windmill graphs, we can gain insights into the behavior of these systems and optimize their performance. In this paper, firstly, we compute the Eccentricity dependent indices by developing suitable partitions of the vertex and the edge set of the generalized windmill graphs. Moreover, to present applications, we define different information functionals and obtain analytical formulae for entropies of generalized windmill graphs. These entropy measures assist us to understand the complexity measures of these graphs. As a specific application, we obtain numeric tables from our proved results which show how the studied model presents the comparison between the complexities of generalized windmill graphs of type I, type II and type III.