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

N1 - Funding Information:
The Authors extend their thanks to the Deanship of Scientific Research at King Khalid University for funding this work through the large group research program under grant number RGP. 2/112/43.
Funding Information:
This research work was supported by the Deanship of Scientific Research at King Khalid University under Grant number RGP. 1/155/42 .
Publisher Copyright:
© 2023

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 - http://www.scopus.com/inward/record.url?scp=85158875906&partnerID=8YFLogxK

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 -