TY - JOUR

T1 - Computing the upper bounds for the metric dimension of cellulose network

AU - Imran, Shahid

AU - Siddiqui, Muhammad Kamran

AU - Imran, Muhammad

AU - Hussain, Muhammad

N1 - Funding Information:
The authors are grateful to the anonymous referees for their valuable comments and suggestions that improved this paper. This research is supported by The Higher Education Commission of Pakistan Under Research and Development Division, National Research Program for Universities via Grant No.: 5348/Federal/NRPU/R&D/HEC/2016. Also, this research is supported by the Start-Up Research Grant 2016 of United Arab Emirates University (UAEU), Al Ain, United Arab Emirates via Grant No. G00002233, UPAR Grant of UAEU via Grant No. G00002590.
Publisher Copyright:
© 2019, Tsing Hua University. All rights reserved.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85077455151

VL - 19

SP - 585

EP - 605

JO - Applied Mathematics E - Notes

JF - Applied Mathematics E - Notes

SN - 1607-2510

ER -