On the Eccentric Connectivity Polynomial of ℱ -Sum of Connected Graphs

Muhammad Imran, Shehnaz Akhter, Zahid Iqbal

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

The eccentric connectivity polynomial (ECP) of a connected graph G=VG,EG is described as ξcG,y=∑a∈VGdegGayecGa, where ecGa and degGa represent the eccentricity and the degree of the vertex a, respectively. The eccentric connectivity index (ECI) can also be acquired from ξcG,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 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.

Original languageEnglish
Article number5061682
JournalComplexity
Volume2020
DOIs
Publication statusPublished - 2020

ASJC Scopus subject areas

  • Computer Science(all)
  • General

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