Some vertex/edge-degree-based topological indices of r-apex trees

• Main Authors: Akbar Ali, Waqas Iqbal, Zahid Raza, Ekram E. Ali, Liu, Jia-Bao, Farooq Ahmad, Qasim Ali Chaudhry
• Other Authors: School of Mechanical and Aerospace Engineering
• Format: Article
• Language: English
• Published: 2021
• Subjects: Engineering::Mechanical engineering; Topological Indices; Graphs
• Online Access: https://hdl.handle.net/10356/154062
• Institution: Nanyang Technological University

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.