TY - JOUR
T1 - On the Eccentric Connectivity Polynomial of ℱ -Sum of Connected Graphs
AU - Imran, Muhammad
AU - Akhter, Shehnaz
AU - Iqbal, Zahid
N1 - 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 -