ON CLASSES OF REGULAR GRAPHS WITH CONSTANT METRIC DIMENSION  

作　　者：Muhammad IMRAN Syed Ahtsham ul Haq BOKHARY Ali AHMAD Andrea SEMANIOV-FENOVíKOV 

机构地区：[1]Centre for Advanced Mathematics and Physics(CAMP),National University of Sciences and Technology(NUST) [2]Center for Advanced Studies in Pure and Applied Mathematics,Bahauddin Zakariya University [3]College of Computer and Information System,Jazan University [4]Department of Applied Mathematics and Informatics,Technical University

出　　处：《Acta Mathematica Scientia》2013年第1期187-206,共20页数学物理学报（B辑英文版）

基　　金：supported by National University of Sceinces and Technology (NUST),Islamabad;grant of Higher Education Commission of Pakistan Ref.No:PMIPFP/HRD/HEC/2011/3386;support of Slovak VEGA Grant 1/0130/12

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 Jn, 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 H5,n by partially answering to an open problem proposed in Ⅱ. 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.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 Jn, 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 H5,n by partially answering to an open problem proposed in Ⅱ. 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.

关 键 词：metric dimension BASIS resolving set cubic graph flower snark convexpolytope 

分 类 号：O157.5[理学—数学] TB911[理学—基础数学]