Wiener Index, Hyper-Wiener Index, Harary Index and Hamiltonicity Properties of graphs

Yu, Guidong; Ren, Lifang; Li, Xing-xing

doi:10.1007/s11766-019-3565-9

Cited by 6 publications

(4 citation statements)

References 13 publications

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“…This method takes into account the distance between vertices when computing the Schultz and modified Schultz indices for trees. Furthermore, Yu et al, [7] extended the research on the Wiener index, providing some of the sufficient conditions for a nearly balanced bipartite graph with a given minimum degree to be traceable. Meanwhile, the Zagreb index has two types: the first Zagreb index and the second Zagreb index.…”

Section: Introductionmentioning

confidence: 99%

The Topological Indices of the p-Subgroup Graph of Dihedral Groups

Fozaiyah Ayed Alhubairah,

Nor Muhainiah Mohd Ali,

Ahmad Erfanian

2024

ARASET

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A topological index is a number generated from a molecular structure that signifies the molecule’s fundamental structural characteristics. This correlation between the index and various physical attributes is based on an algebraic quantity related to the chemical structure. Many topological indices, such as the Wiener index, first and second Zagreb indices, can be employed to determine various properties, including chemical activity, thermodynamic properties, physicochemical activity, and biological activity. Meanwhile, the p-subgroup graph of a group G is defined as a graph whose vertices represent the elements of the group, and two vertices are adjacent if and only if the order of the subgroup is a prime power. The main objective of this paper is to establish the general formula for certain topological indices, specifically the Wiener index, first Zagreb index, and second Zagreb index for the -subgroup graph associated with dihedral groups.

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Section: Introductionmentioning

confidence: 99%

The Topological Indices of the p-Subgroup Graph of Dihedral Groups

Fozaiyah Ayed Alhubairah,

Nor Muhainiah Mohd Ali,

Ahmad Erfanian

2024

ARASET

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“…This latter, which is also the subject of our paper, gives more weights on the expansive parts of the graph than the Wiener index and finds uses in quantum chemistry and mathematics as well. A variety of indices can be used to describe different aspects of graphs [12]. These topological graph indices are widely used mathematical tools, used by physicists, chemists and engineers for molecule descriptions.…”

Section: Introductionmentioning

confidence: 99%

The hyper‐Wiener Index of diamond nanowires

Nagy

2023

Int J of Quantum Chemistry

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Carbon nanowires based on various structures have various applications. In this article, our focus is on diamond nano‐wires, based on the structure of the diamond. Our goal is to characterize these nanowires by providing their hyper‐Wiener index, one of the basic topological graph indices. The diamond is formed by carbon atoms in a compact structure: every atom has exactly four neighbors connected by covalent bonds according to the simplest three‐dimensional polyhedron. Considering an atom in the center of a tetrahedron, its neighbors, the atoms connected to it by bonds, are located in the corners of the tetrahedron. In this article, this “diamond‐grid” structure is analysed in the case that the graphs correspond to connected parts of sequences of unit cells, in this way forming nanowires of various lengths. By a combinatorial approach, a closed formula is proven for the hyper‐Wiener index based on the graph‐distances of every pair of carbon atoms (i.e., the minimal number of edges connecting the atoms), and this formula depends only on the size of the graph in terms of the number of unit cells included.

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“…Especially, some topological indices are used to characterize the Hamiltonian property of graphs. We refer readers to see [2,[12][13][14][15][16][17][18][19][20][21]. Among them, Hua and Ning [15] gave Hamiltonian conditions for a balanced bipartite graph with respect to the Wiener index and Harary index.…”

Section: Introductionmentioning

confidence: 99%

“…Li [18,19] gave Hamitonian conditions for a t-connected graph with respect to the Wiener index and Harary index, respectively. With the Wiener index, hyper-Wiener index, and Harary index, Yu et al [20] gave conditions for a tconnected graph to be Hamilton-connected and then got conditions for it to be traceable from every vertex, as well as gave conditions for a nearly balance bipartite graph to be traceable. Especially, Liu et al [16,17] studied the Hamiltonian property of graphs with respect to the Wiener index and Harary index of complement of graph or quasicomplement of bipartite graph, respectively.…”

Section: Introductionmentioning

confidence: 99%

Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index

Jiang

Ren

2019

Journal of Chemistry

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In this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or traceable for every vertex. Firstly, we discuss balanced bipartite graphs with δG≥t, where δG is the minimum degree of G, and gain some sufficient conditions for the graphs to be traceable or Hamiltonian, respectively. Secondly, we discuss nearly balanced bipartite graphs with δG≥t and present some sufficient conditions for the graphs to be traceable. Thirdly, we discuss graphs with δG≥t and obtain some conditions for the graphs to be traceable or Hamiltonian, respectively. Finally, we discuss t-connected graphs and provide some conditions for the graphs to be Hamilton-connected or traceable for every vertex, respectively.

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Wiener Index, Hyper-Wiener Index, Harary Index and Hamiltonicity Properties of graphs

Cited by 6 publications

References 13 publications

The Topological Indices of the p-Subgroup Graph of Dihedral Groups

The Topological Indices of the p-Subgroup Graph of Dihedral Groups

The hyper‐Wiener Index of diamond nanowires

Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index

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