Computing the upper bounds for the metric dimension of cellulose network

Shahid Imran, Muhammad Kamran Siddiqui, Muhammad Imran, Muhammad Hussain

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). In this paper we study three dimensional chemical structure of cellulose network and then we converted it into planar chemical structure, consequently we obtained cellulose network graphs denoted by CLkn. We prove that dim(CLkn) ≤ 4 in certain cases.

Original languageEnglish
Pages (from-to)585-605
Number of pages21
JournalApplied Mathematics E - Notes
Volume19
Publication statusPublished - 2019

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Computing the upper bounds for the metric dimension of cellulose network'. Together they form a unique fingerprint.

Cite this