The Wiener index, degree distance index and Gutman index of composite hypergraphs and sunflower hypergraphs

Ashraf, Sakina; Imran, Muhammad; Bokhary, Syed Ahtsham Ul Haq; Akhter, Shehnaz

doi:10.1016/j.heliyon.2022.e12382

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…In [8], Das et al generalized the well-known Gutman index by introducing the general Gutman index of a graph. The recent literature has discussed the association and comparison between the degree distance and Gutman index [9][10][11], respectively. The extremal generalized Gutman index of trees was studied in [12].…”

Section: Introductionmentioning

confidence: 99%

The Vertex Gutman Index and Gutman Index of the Union of Two Cycles

Mei,

Miao

2024

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The Wiener index is one of the most classic and widely used indicators in topology. It reflects the average distance of any node pair in the graph. It not only makes the boundaries of given graphs clearer but also continuously generates topological indices that are more suitable for new fields, such as the Gutman index. The Wiener index and Gutman index are two important topological indices, which are commonly used to describe the characteristics of molecular structure. They are closely related to the physical and chemical properties of molecular compounds. And they are widely used to predict the physical and chemical properties and biological activity of molecular compounds. In this paper, we study the vertex Gutman index and Gutman index and describe the structural characteristics of all cases of two simple cycles intersecting. We comprehensively analyze the Gutman index and vertex Gutman index in these cases in detail by means of classification discussion and analogical reasoning and characterize their maximum and minimum accordingly.

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Section: Introductionmentioning

confidence: 99%

The Vertex Gutman Index and Gutman Index of the Union of Two Cycles

Mei,

Miao

2024

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“…The effect of some transformations on the Wiener index of a hypergraph and extremal hypertrees with respect to the Wiener index is studied in [25]. The k-uniform unicyclic hypergraphs with maximum/minimum and second maximum/minimum Wiener index are determined in [35], while the Wiener index of some composite hypergraphs and sunflower hypergraphs is the topic of [5]. Finally, in [8] the concept of the k-Wiener index is introduced and studied on the so called k-plex hypergraphs, while in [36] the maximum possible Wiener index of a connected n-vertex k-uniform hypergraph has been determined and the extremal graphs characterized.…”

Section: Introductionmentioning

confidence: 99%

The cut method on hypergraphs for the Wiener index

Klavžar

Romih

2023

J Math Chem

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The cut method has been proved to be extremely useful in chemical graph theory. In this paper the cut method is extended to hypergraphs. More precisely, the method is developed for the Wiener index of k-uniform partial cube-hypergraphs. The method is applied to cube-hypergraphs and hypertrees. Extensions of the method to hypergraphs arising in chemistry which are not necessary k-uniform and/or not necessary linear are also developed.

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Computation of Wiener and Wiener Polarity Indices of a Class of Nanostar Dendrimer Using Vertex Weighted Graphs

Bokhary,

Bashir,

Nawaz

et al. 2024

Journal of Mathematics

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Nanostar dendrimers are tree-like nanostructures with a well-defined, symmetrical architecture. They are built in a step-by-step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell. A weighted graph is a type of graph in which vertices or edges are assigned weights that represent cost, distance, and a variety of other relative measuring units. The weighted graphs have many applications and properties in a mathematical context. The topological indices are numerical values that represent the symmetry of a molecular structure. They have rich applications in theoretical chemistry. Various topological indices can be used to investigate a wide range of properties of chemical compounds with a molecular structure. They are very important in mathematical chemistry, especially in quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies. In this paper, we examine the topological properties of the molecular graphs of nanostar dendrimers. For this purpose, the topological indices, namely, the Wiener index and the Wiener polarity index are computed for a class of nanostar dendrimers.

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The Wiener index, degree distance index and Gutman index of composite hypergraphs and sunflower hypergraphs

Cited by 4 publications

References 25 publications

The Vertex Gutman Index and Gutman Index of the Union of Two Cycles

The Vertex Gutman Index and Gutman Index of the Union of Two Cycles

The cut method on hypergraphs for the Wiener index

Computation of Wiener and Wiener Polarity Indices of a Class of Nanostar Dendrimer Using Vertex Weighted Graphs

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