On Wiener index and Wiener polarity index of some polyomino chains

Sarfraz Ahmad; Hafiz Muhammad Afzal Siddiqui; Arfan Ali; Mohammad R. Farahani; Muhammad Imran; Ismail Naci Cangul

doi:10.1080/09720529.2019.1688965

On Wiener index and Wiener polarity index of some polyomino chains

Sarfraz Ahmad, Hafiz Muhammad Afzal Siddiqui, Arfan Ali, Mohammad R. Farahani, Muhammad Imran, Ismail Naci Cangul

Department of Mathematical Sciences

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

31 Citations (Scopus)

Abstract

A graph invariant is a numerical value that depicts the structural properties of an entire graph. The Wiener index is the oldest distance based graph invariant which is defined as the sum of distances between all unordered pair of vertices of the graph G. In this paper we use the method of edge cut to compute the Wiener index and Wiener polarity index of linear (L_n) and zig-zag (Z_n) polyomino chains of 4-cycle. Also, we introduce another polyomino chain of 4k-cycle Z_mn and calculate its Wiener index and Wiener polarity index for m = 3 and m = 4. Finally, the graphical representation is given to analyze the behavior of these indices.

Original language	English
Pages (from-to)	1151-1164
Number of pages	14
Journal	Journal of Discrete Mathematical Sciences and Cryptography
Volume	22
Issue number	7
DOIs	https://doi.org/10.1080/09720529.2019.1688965
Publication status	Published - Oct 3 2019

Keywords

05C12
37B30
Graph invariant
Wiener index
Wiener polarity index
linear chains
polyomino chains
zig-zag chains

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/09720529.2019.1688965

Cite this

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abstract = "A graph invariant is a numerical value that depicts the structural properties of an entire graph. The Wiener index is the oldest distance based graph invariant which is defined as the sum of distances between all unordered pair of vertices of the graph G. In this paper we use the method of edge cut to compute the Wiener index and Wiener polarity index of linear (Ln) and zig-zag (Zn) polyomino chains of 4-cycle. Also, we introduce another polyomino chain of 4k-cycle Zmn and calculate its Wiener index and Wiener polarity index for m = 3 and m = 4. Finally, the graphical representation is given to analyze the behavior of these indices.",

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AU - Ali, Arfan

AU - Farahani, Mohammad R.

AU - Imran, Muhammad

AU - Cangul, Ismail Naci

PY - 2019/10/3

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On Wiener index and Wiener polarity index of some polyomino chains

Abstract

Keywords

ASJC Scopus subject areas

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