TY - JOUR

T1 - On the Eccentric Connectivity Polynomial of ℱ -Sum of Connected Graphs

AU - Imran, Muhammad

AU - Akhter, Shehnaz

AU - Iqbal, Zahid

N1 - Funding Information:
This research was supported by UPAR Grant of United Arab Emirates University (UAEU), Al Ain, UAE, via Grant nos. G00002590 and G00003271.
Publisher Copyright:
© 2020 Muhammad Imran et al.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1155/2020/5061682

DO - 10.1155/2020/5061682

M3 - Article

AN - SCOPUS:85086857205

SN - 1076-2787

VL - 2020

JO - Complexity

JF - Complexity

M1 - 5061682

ER -