On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected Graphs
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 der...
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/5061682 |
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| author | Muhammad Imran Shehnaz Akhter Zahid Iqbal |
| author_facet | Muhammad Imran Shehnaz Akhter Zahid Iqbal |
| author_sort | Muhammad Imran |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f368d1898f4d47deb7b8c153917be521 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f368d1898f4d47deb7b8c153917be5212025-02-03T01:04:40ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/50616825061682On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected GraphsMuhammad Imran0Shehnaz Akhter1Zahid Iqbal2Department of Mathematical Sciences, College of Science, United Arab Emirates University, P.O. Box 15551, Al Ain, UAEDepartment of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, PakistanDepartment of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, PakistanThe 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.http://dx.doi.org/10.1155/2020/5061682 |
| spellingShingle | Muhammad Imran Shehnaz Akhter Zahid Iqbal On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected Graphs Complexity |
| title | On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected Graphs |
| title_full | On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected Graphs |
| title_fullStr | On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected Graphs |
| title_full_unstemmed | On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected Graphs |
| title_short | On the Eccentric Connectivity Polynomial of ℱ-Sum of Connected Graphs |
| title_sort | on the eccentric connectivity polynomial of f sum of connected graphs |
| url | http://dx.doi.org/10.1155/2020/5061682 |
| work_keys_str_mv | AT muhammadimran ontheeccentricconnectivitypolynomialoffsumofconnectedgraphs AT shehnazakhter ontheeccentricconnectivitypolynomialoffsumofconnectedgraphs AT zahidiqbal ontheeccentricconnectivitypolynomialoffsumofconnectedgraphs |