Wiener polarity and Wiener index of double generalized Petersen graph

Tanveer Iqbal; Syed Ahtsham Ul Haq Bokhary; Ghulam Abbas; Jamel Baili; Hijaz Ahmad; Hafsah Tabassum; Saqib Murtaza; Zubair Ahmad; Xiao Zhong Zhang

doi:10.1016/j.jksus.2023.102680

Wiener polarity and Wiener index of double generalized Petersen graph

Tanveer Iqbal
, Syed Ahtsham Ul Haq Bokhary
, Ghulam Abbas
, Jamel Baili
, Hijaz Ahmad
, Hafsah Tabassum
, Saqib Murtaza
, Zubair Ahmad
, Xiao Zhong Zhang

Research output: Contribution to journal › Article › peer-review

Abstract

A topological index is a numerical parameter of a graph which characterizes some of the topological properties of the graph. The concepts of Wiener polarity index and Wiener index were established in chemical graph theory by means of the distances. The double generalized Petersen graph denoted by DP(n,k) is obtained by attaching the vertices of outer pendent vertices to inner pendent vertices lying at distance k. The length of the outer and inner cycle is n, thus the number of vertices are 4n and the number of edges in the DP(n,k) are 6n. In this paper, the Wiener polarity index of DP(n,k for 3≤n≤6 and for n≥6k+1 is computed. Further, the Wiener index of DP(n,k), for k={1,2} is determined.

Original language	English (US)
Article number	102680
Journal	Journal of King Saud University - Science
Volume	35
Issue number	5
DOIs	https://doi.org/10.1016/j.jksus.2023.102680
Publication status	Published - Jul 2023
Externally published	Yes

Keywords

Double Generalized Petersen Graph
Wiener Index
Wiener Polarity Index

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10.1016/j.jksus.2023.102680

Cite this

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title = "Wiener polarity and Wiener index of double generalized Petersen graph",

abstract = "A topological index is a numerical parameter of a graph which characterizes some of the topological properties of the graph. The concepts of Wiener polarity index and Wiener index were established in chemical graph theory by means of the distances. The double generalized Petersen graph denoted by DP(n,k) is obtained by attaching the vertices of outer pendent vertices to inner pendent vertices lying at distance k. The length of the outer and inner cycle is n, thus the number of vertices are 4n and the number of edges in the DP(n,k) are 6n. In this paper, the Wiener polarity index of DP(n,k for 3≤n≤6 and for n≥6k+1 is computed. Further, the Wiener index of DP(n,k), for k=\{1,2\} is determined.",

keywords = "Double Generalized Petersen Graph, Wiener Index, Wiener Polarity Index",

author = "Tanveer Iqbal and \{Ahtsham Ul Haq Bokhary\}, Syed and Ghulam Abbas and Jamel Baili and Hijaz Ahmad and Hafsah Tabassum and Saqib Murtaza and Zubair Ahmad and Zhang, \{Xiao Zhong\}",

note = "Publisher Copyright: {\textcopyright} 2023",

year = "2023",

month = jul,

doi = "10.1016/j.jksus.2023.102680",

language = "English (US)",

volume = "35",

journal = "Journal of King Saud University - Science",

issn = "1018-3647",

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number = "5",

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TY - JOUR

T1 - Wiener polarity and Wiener index of double generalized Petersen graph

AU - Iqbal, Tanveer

AU - Ahtsham Ul Haq Bokhary, Syed

AU - Abbas, Ghulam

AU - Baili, Jamel

AU - Ahmad, Hijaz

AU - Tabassum, Hafsah

AU - Murtaza, Saqib

AU - Ahmad, Zubair

AU - Zhang, Xiao Zhong

PY - 2023/7

Y1 - 2023/7

N2 - A topological index is a numerical parameter of a graph which characterizes some of the topological properties of the graph. The concepts of Wiener polarity index and Wiener index were established in chemical graph theory by means of the distances. The double generalized Petersen graph denoted by DP(n,k) is obtained by attaching the vertices of outer pendent vertices to inner pendent vertices lying at distance k. The length of the outer and inner cycle is n, thus the number of vertices are 4n and the number of edges in the DP(n,k) are 6n. In this paper, the Wiener polarity index of DP(n,k for 3≤n≤6 and for n≥6k+1 is computed. Further, the Wiener index of DP(n,k), for k={1,2} is determined.

AB - A topological index is a numerical parameter of a graph which characterizes some of the topological properties of the graph. The concepts of Wiener polarity index and Wiener index were established in chemical graph theory by means of the distances. The double generalized Petersen graph denoted by DP(n,k) is obtained by attaching the vertices of outer pendent vertices to inner pendent vertices lying at distance k. The length of the outer and inner cycle is n, thus the number of vertices are 4n and the number of edges in the DP(n,k) are 6n. In this paper, the Wiener polarity index of DP(n,k for 3≤n≤6 and for n≥6k+1 is computed. Further, the Wiener index of DP(n,k), for k={1,2} is determined.

KW - Double Generalized Petersen Graph

KW - Wiener Index

KW - Wiener Polarity Index

UR - https://www.scopus.com/pages/publications/85158875906

U2 - 10.1016/j.jksus.2023.102680

DO - 10.1016/j.jksus.2023.102680

M3 - Article

AN - SCOPUS:85158875906

SN - 1018-3647

VL - 35

JO - Journal of King Saud University - Science

JF - Journal of King Saud University - Science

IS - 5

M1 - 102680

ER -

Wiener polarity and Wiener index of double generalized Petersen graph

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Keywords

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