On Weighted PI Index of Graphs

Pattabiraman, K.; Kandan, P.

doi:10.1016/j.endm.2016.05.020

Cited by 11 publications

(7 citation statements)

References 17 publications

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“…For a survey of results on Wiener index, Wiener polarity index and some other variations of Wiener index, see [23]. The study of topological indices for several graph operations has been carried out in the literature, for example see [14,[24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Topological Indicesmentioning

confidence: 99%

Wiener polarity and similar topological descriptors of some product graphs

Haoer

2021

Int J of Quantum Chemistry

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The leap Zagreb and Wiener polarity indices are computed from the information of second and third distances in a graph. Like many other topological indices defined in the literature, these indices are important for their applications in quantitative structure‐property relationship studies. In this paper, we compute these indices of a graph product known as subdivision vertex‐edge join of three graphs, which is also known as SVE‐join of graphs. We also compute the leap Zagreb coindices of these graphs.

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Section: Topological Indicesmentioning

confidence: 99%

Wiener polarity and similar topological descriptors of some product graphs

Haoer

2021

Int J of Quantum Chemistry

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“… and Refs. , respectively. However, it seems natural to consider also the weighted edge‐Szeged index and the weighted PI index :

\begin{matrix} {right left}true \\ {italicwSz}_{e} (G) = \underset{e = uv \in E (G)}{false\sum} (\deg (u) + \deg (v)) m_{u} (e) m_{v} (e), \\ wPI (G) = \underset{e = uv \in E (G)}{false\sum} (\deg (u) + \deg (v)) (m_{u} (e) + m_{v} (e)) . \end{matrix}

…”

Section: Introductionmentioning

confidence: 98%

“…For some research on these indices see [3,25,27,28] and [23,24,26,34], respectively. However, it seems natural to consider also the weighted edge-Szeged index and the weighted PI index :…”

Section: Introductionmentioning

confidence: 99%

Computing weighted Szeged and PI indices from quotient graphs

Tratnik

2019

Int J of Quantum Chemistry

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The weighted (edge‐)Szeged index and the weighted (vertex‐)PI index are modifications of the (edge‐)Szeged index and the (vertex‐)PI index, respectively, because they take into account also the vertex degrees. As the main result of this article, we prove that if G is a connected graph, then all these indices can be computed in terms of the corresponding indices of weighted quotient graphs with respect to a partition of the edge set that is coarser than the Θ*‐partition. If G is a benzenoid system or a phenylene, then it is possible to choose a partition of the edge set in such a way that the quotient graphs are trees. As a consequence, it is shown that for a benzenoid system, the mentioned indices can be computed in sublinear time with respect to the number of vertices. Moreover, closed formulas for linear phenylenes are also deduced.

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“…Additionally, for n −vertex unicyclic graphs with a certain diameter, Wang et al [16] identified their minimum edge-Szeged index in 2018. Pattabiraman and Kandan have introduced the weighted Szeged index of a splice graph and link graph [17]. Meanwhile, in 2022, Liu [18] discovered the smallest revised Szeged index among all conjugated unicyclic graphs.…”

Section: Introductionmentioning

confidence: 99%

On the Szeged Index and Its Non-Commuting Graph

2023

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In chemistry, the molecular structure can be represented as a graph. Based on the information from the graph, its characterization can be determined by computing the topological index. Topological index is a numerical value that can be computed by using some algorithms and properties of the graph. Meanwhile, the non-commuting graph is a graph, in which two distinct vertices are adjacent if and only if they do not commute, where it is made up of the non-central elements in a group as a vertex set. In this paper, the Szeged index of the non-commuting graph of some finite groups are computed. This paper focuses on three finite groups which are the quasidihedral groups, the dihedral groups, and the generalized quaternion groups. The construction of the graph is done by using Maple software. In finding the Szeged index, some of the previous results and properties of the graph for the quasidihedral groups, the dihedral groups, and the generalized quaternion groups are used. The generalisation of the Szeged index of the non-commuting graph is then established for the aforementioned groups. The results are then applied to find the Szeged index of the non-commuting graph of ammonia molecule.

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On Weighted PI Index of Graphs

Cited by 11 publications

References 17 publications

Wiener polarity and similar topological descriptors of some product graphs

Wiener polarity and similar topological descriptors of some product graphs

Computing weighted Szeged and PI indices from quotient graphs

On the Szeged Index and Its Non-Commuting Graph

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