The cut method on hypergraphs for the Wiener index

Klavžar, Sandi; Romih, Gašper Domen

doi:10.1007/s10910-023-01478-4

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…The oldest topological index in chemical graph theory is the Wiener index [15]. Despite being introduced in 1947 and studied ever since, it still generates a lot of interest [5,6,9,10,12,14,16,17,18]. For a connected graph G, its Wiener index is defined as…”

Section: Introductionmentioning

confidence: 99%

Extremal trees with respect to bi-Wiener index

Chen,

Karimi,

et al. 2024

Preprint

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In this paper we introduce and study a new graph-theoretic invariant called the bi-Wiener index. The bi-Wiener index Wb(G) of a bipartite graph G is defined as the sum of all (shortest-path) distances between two vertices from different parts of the bipartition of the vertex set of G. We start with providing a motivation connected with the potential uses of the new invariant in the QSAR/QSPR studies. Then we study its behavior for trees. We prove that, among all trees of order n ≥ 4, the minimum value of Wb is attained for the star Sn, and the maximum Wb is attained at Pn for even n, or at Pn and Bn(2) for odd n where Bn(2) is a broom with maximum degree 3. We also determine the extremal values of the ratio Wb(Tn)/W(Tn) over all trees on a given number of vertices n. At the end, we indicate some open problems and discuss some possible directions of further research. AMS Subj. Class. (2020): 05C05, 05C09, 05C12, 05C92

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Section: Introductionmentioning

confidence: 99%

Extremal trees with respect to bi-Wiener index

Chen,

Karimi,

et al. 2024

Preprint

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“…A significant contribution to the knowledge concerning the Wiener index and other topological indices was accumulated in the survey papers. [10]- [18] In this paper, we found the Wiener index of acrylate and methacrylate polymer based on their molecular structure. Also we have used the Wiener index to predict the boiling point of acrylate and methacrylate polymers.…”

Section: Introductionmentioning

confidence: 99%

Prediction of the Boiling Point of Acrylate and Methacrylate Polymers Through Wiener Index

Ezhilan,

Varadhan

2024

MATCH

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Wiener index, a topological index of a molecular graph of the molecules are widely used to study the physico-chemical properties of the molecules. We considered the molecules, acrylate and methacrylate polymers. The Wiener index of these two polymers are obtained. And using this, the boiling point of these two polymers are studied extensively. Also, the detailed comparison is described graphically.

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Extremal Trees with Respect to Bi-Wiener Index

Chen,

Karimi,

et al. 2024

Bull. Malays. Math. Sci. Soc.

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The cut method on hypergraphs for the Wiener index

Cited by 3 publications

References 32 publications

Extremal trees with respect to bi-Wiener index

Extremal trees with respect to bi-Wiener index

Prediction of the Boiling Point of Acrylate and Methacrylate Polymers Through Wiener Index

Extremal Trees with Respect to Bi-Wiener Index

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