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

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...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2021, Vol.2021, p.1-8
Main Authors: Ali, Akbar, Iqbal, Waqas, Raza, Zahid, Ali, Ekram E., Liu, Jia-Bao, Ahmad, Farooq, Chaudhry, Qasim Ali
Format: Article
Language:English
Subjects:
Apexes
Connectivity
Graph theory
Inequality
Mathematics
Numbers
Terminology
Topology
Trees
Trees (mathematics)
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/4349074