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On the Eccentric Connectivity Polynomial of - Sum of Connected Graphs

Author

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  • Muhammad Imran
  • Shehnaz Akhter
  • Zahid Iqbal

Abstract

The eccentric connectivity polynomial (ECP) of a connected graph is described as , where and represent the eccentricity and the degree of the vertex , respectively. The eccentric connectivity index (ECI) can also be acquired from by taking its first derivatives at . 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 - 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.

Suggested Citation

  • Muhammad Imran & Shehnaz Akhter & Zahid Iqbal, 2020. "On the Eccentric Connectivity Polynomial of - Sum of Connected Graphs," Complexity, Hindawi, vol. 2020, pages 1-9, May.
    • Handle: RePEc:hin:complx:5061682
    DOI: 10.1155/2020/5061682
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