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Operations Research Transactions >

2025 , Vol. 29 >Issue 1: 207 - 215

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.01.017

On harmonic index of trees with fixed domination number

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  • 1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China

Received date: 2021-09-08

  Online published: 2025-03-08

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, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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Abstract

In order to predict the physical, chemical properties and biological activities of molecules, scientists have proposed many topological indices. As a variant of the well known Randićindex, the harmonic index is proven to be a valuable predictive index in the study of the physical and chemical properties of compounds. The harmonic index of trees with fixed domination number was investigated. By analyzing the structure of trees with fixed domination number and using the method of mathematical induction, the maximum and minimum harmonic indices of trees with fixed domination number are presented. Furthermore, the corresponding extremal trees are determined.

Key words： harmonic index; tree; domination number

Cite this article

Xiaoling SUN, Yubin GAO, Jianwei DU . On harmonic index of trees with fixed domination number[J]. Operations Research Transactions, 2025 , 29(1) : 207 -215 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.01.017

References

1 Gutman I , Furtula B . Novel Molecular Structure Descriptors——Theory and Applications Ⅰ[M]. Kragujevac: University of Kragujevac, 2010.
2 Gutman I , Furtula B . Novel Molecular Structure Descriptors——Theory and Applications Ⅱ[M]. Kragujevac: University of Kragujevac, 2010.
3 Todeschini R , Consonni V . Handbook of Molecular Descriptors[M]. Weinheim: Wiley-VCH, 2000.
4 Fajtlowicz S . On conjectures of Graffiti-Ⅱ[J]. Congressus Numerantium, 1987, 60, 187- 197.
5 Ore O . Theory of Graphs[M]. Providence: American Mathematical Society, 1962.
6 Fink J F , Jacobson M S , Kinch L F , et al. On graphs having domination number half their order[J]. Periodica Mathematica Hungarica, 1985, 16, 287- 293.
7 Bondy J A , Murty U S R . Graph Theory with Applications[M]. New York: Elsvier, 1976.
8 Abdolghafourian A , Iranmanesh M A . The minimum harmonic index for bicyclic graphs with given diameter[J]. Filomat, 2022, 36, 125- 140.
9 Abdolghafourian A , Iranmanesh M A . On harmonic index and diameter of quasi-tree graphs[J]. Journal of Mathematics, 2021, 2021, 6650407.
10 LYU J , Li J . The harmonic index of a graph and its DP-chromatic number[J]. Discrete Applied Mathematics, 2020, 284, 611- 615.
11 Ali A , Zhong L , Gutman I . Harmonic index and its generalizations: extremal results and bounds[J]. MATCH-Communications in Mathematical and in Computer Chemistry, 2019, 81, 249- 311.
12 Boroviéanin B , Furtula B . On extremal Zagreb indices of trees with given domination number[J]. Applied Mathematics and Computation, 2016, 279, 208- 218.
13 Dankelmann P . Average distance and domination number[J]. Discrete Applied Mathematics, 1997, 80, 21- 35.
14 Bermudo S , Nápoles J E , Rada J . Extremal trees for the Randi?index with given domination number[J]. Applied Mathematics and Computation, 2020, 375, 125122.
15 He C , Wu B , Yu Z . On the energy of trees with given domination number[J]. MATCH-Communications in Mathematical and in Computer Chemistry, 2010, 64, 169- 180.
16 Li S , Meng X . Four edge-grafting theorems on the reciprocal degree distance of graphs and their applications[J]. Journal of Combinatorial Optimization, 2015, 30, 468- 488.
17 Li S , Zhang H . Some extremal properties of the multiplicatively weighted Harary index of a graph[J]. Journal of Combinatorial Optimization, 2016, 31, 961- 978.
18 Sun X , Du J . On Sombor index of trees with fixed domination number[J]. Applied Mathematics and Computation, 2022, 421, 611- 615.
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