ON CLASSES OF REGULAR GRAPHS WITH CONSTANT METRIC DIMENSION

被引：41

作者：

Imran, Muhammad ^{[1
]}

Bokhary, Syed Ahtsham ul Haq ^{[2
]}

Ahmad, Ali ^{[3
]}

Semanicova-Fenovcikova, Andrea ^{[4
]}

机构：

[1] NUST, CAMP, Islamabad, Pakistan

[2] Bahauddin Zakariya Univ, Ctr Adv Studies Pure & Appl Math, Multan, Pakistan

[3] Jazan Univ, Coll Comp & Informat Syst, Jazan, Saudi Arabia

[4] Tech Univ, Dept Appl Math & Informat, Kosice 04200, Slovakia

来源：

ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 01期

关键词：

metric dimension; basis; resolving set; cubic graph; flower snark; convex polytope; FAMILIES;

D O I：

10.1016/S0252-9602(12)60204-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks J(n), a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H-5,H-n by partially answering to an open problem proposed in [I. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88: 43-57]. We prove that these classes of regular graphs have constant metric dimension.

引用

页码：187 / 206

页数：20

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