The harmonic index for trees with given domination number | [Discrete Mathematics Letters • 2022]

Author(s):

1. Xipeng Hu: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China; Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing , China

2. Lingping Zhong: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China; Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing , China

Abstract:

For a graph G, let uv be an edge of G. The weight of uv is defined as 2(d(u) + d(v)) 1, where d(u) and d(v) denote the degree of the vertices u and v, respectively. In this paper, we consider the harmonic index H(G) which is the sum of weights of all edges of G, and obtain the extremal values of trees in terms of the order and domination number of G. We also characterize the extremal trees

Page(s): 31-37

DOI: 10.47443/dml.2021.s206

Published: Journal: Discrete Mathematics Letters, Volume: 9, Issue: 0, Year: 2022

Keywords:

Tree , domination number , harmonic index

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