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

Research output: Contribution to journalArticlepeer-review

29 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 (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.

Original languageEnglish
Pages (from-to)1151-1164
Number of pages14
JournalJournal of Discrete Mathematical Sciences and Cryptography
Volume22
Issue number7
DOIs
Publication statusPublished - 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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