Zagreb Eccentricity Indices of Cycles Related Graphs

Abstract

Graph theory, with its diverse applications in theoretical computer science and in natural sciences (chemistry, biology), is becoming an important component of mathematics. Recently, the concepts of new Zagreb eccentricity indices were introduced. These indices were defined for any graph \(G\), as follows: \(M_1^*(G) = \sum_{e_{uv} \in E(G)} [\varepsilon_G(u) + \varepsilon_G(v)]\), \(M_1^{**}(G) = \sum_{v \in V(G)} [\varepsilon_G(v)]^2\), and \(M_2^*(G) = \sum_{e_{uv} \in E(G)} |\varepsilon_G(u) – \varepsilon_G(v)|\), where \(\varepsilon_G(u)\) is the eccentricity value of vertex \(u\) in the graph \(G\). In this paper, new Zagreb eccentricity indices \(M_1^*(G)\), \(M_1^{**}(G)\), and \(M_2^*(G)\) of cycles related graphs, namely gear, friendship, and corona graphs, are determined. Then, a programming code finding values of new Zagreb indices of any graph is offered.