Some Vertex/Edge-Degree-Based Topological Indices of r-Apex Trees

Akbar Ali, Waqas Iqbal, Zahid Raza, Ekram E. Ali, Jia-Bao Liu, Farooq Ahmad, Qasim Ali Chaudhry and Muhammad Kamran Siddiqui

Journal of Mathematics, 2021, vol. 2021, 1-8

Abstract: In chemical graph theory, graph invariants are usually referred to as topological indices. For a graph G, its vertex-degree-based topological indices of the form BIDG=∑uv∈EGβdu,dv are known as bond incident degree indices, where EG is the edge set of G, dw denotes degree of an arbitrary vertex w of G, and β is a real-valued-symmetric function. Those BID indices for which β can be rewritten as a function of du+dv−2 (that is degree of the edge uv) are known as edge-degree-based BID indices. A connected graph G is said to be r-apex tree if r is the smallest nonnegative integer for which there is a subset R of VG such that R=r and G−R is a tree. In this paper, we address the problem of determining graphs attaining the maximum or minimum value of an arbitrary BID index from the class of all r-apex trees of order n, where r and n are fixed integers satisfying the inequalities n−r≥2 and r≥1.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4349074

DOI: 10.1155/2021/4349074

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