Distance-Based Connectivity Indices for Chain Polygonal Cactus Networks and Their Applications in Wireless Communication Systems

Distance-Based Connectivity Indices in CPC

Abstract

This paper develops two novel distance-based connectivity indices for Chain Polygonal Cactus (CPC) networks, a class of graphs formed by linking cycles via articulation points. We define the d-connectivity index, which characterizes short-range communication potential through degree–distance analysis, and the e-connectivity index, which reflects long-range connectivity based on eccentricity–distance relationships. Exact analytical formulas for these indices are derived for various structural configurations of CPCs by systematically partitioning the vertex sets according to their combinatorial and distance properties. The theoretical results not only advance the study of distance-based invariants in graph theory but also motivate applications in wireless communication systems, where CPC-like topologies can enhance network efficiency and resilience. Our findings provide a mathematical framework for assessing structural robustness and accessibility in networked systems.