an:07241512
Zbl 1441.05126
Imran, Muhammad; Akhter, Shehnaz; Iqbal, Zahid
On the eccentric connectivity polynomial of \(\mathcal{F}\)-sum of connected graphs
EN
Complexity 2020, Article ID 5061682, 9 p. (2020).
00444991
2020
j
05C40 05C31 05C76
Summary: The eccentric connectivity polynomial (ECP) of a connected graph \(G=(V(G), E(G\)) is described as \(\xi^c G\), \(y= \sum_{a\in V(G)} \deg_G (a)y^{e c_G(a)}\), where \(e c_G(a)\) and \(\deg_G(a)\) represent the eccentricity and the degree of the vertex \(a\), respectively. The eccentric connectivity index (ECI) can also be acquired from \(\xi^c(G,y)\) by taking its first derivatives at \(y=1\). The ECI has been widely used for analyzing both the boiling point and melting point for chemical compounds and medicinal drugs in QSPR/QSAR studies. As the extension of ECI, the ECP also performs a pivotal role in pharmaceutical science and chemical engineering. Graph products conveniently play an important role in many combinatorial applications, graph decompositions, pure mathematics, and applied mathematics. In this article, we work out the ECP of \(\mathcal{F}\)-sum of graphs. Moreover, we derive the explicit expressions of ECP for well-known graph products such as generalized hierarchical, cluster, and corona products of graphs. We also apply these outcomes to deduce the ECP of some classes of chemical graphs.