Topological Index in Shadow Graphs
Articles > Article · 2025
Authors: Aysun AYTAÇ, Rabia Nur Karslı
Boletim da Sociedade Paranaense de Matemática, International, Scopus, 2025, vol 43, pp 1-9
DOI: 10.5269/bspm.69761
Summary
Mathematical modeling of various natural biological activities has gained significant importance in recent times. In the modeling of these activities, the eccentric connectivity index (ECI) is utilized as a distance-based molecular structure descriptor. This index is defined as ${{\varepsilon }^{c}}(G)=\sum\limits_{v\in V(G)}{\deg (v)e(v)}$, where $\deg (v)$ and $e(v)$ denote the vertex degree and eccentricity of $v$, respectively. To support its use as a topological structure descriptor, this study calculates the ECI values of shadow graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.