|
|||||
|
|
ON CLASSES OF REGULAR GRAPHS WITH CONSTANT METRIC DIMENSION |
|
| Authors: | Muhammad IMRAN Syed Ahtsham ul Haq BOKHARY Ali AHMAD Andrea SEMANIOV-FEOVKOV |
| Institution: | 1. Centre for Advanced Mathematics and Physics(CAMP), National University of Sciences and Technology(NUST), Sector H-12, Islamabad, Pakistan 2. Center for Advanced Studies in Pure and Applied Mathematics,Bahauddin Zakariya University, Multan, Pakistan 3. College of Computer and Information System, Jazan University, Jazan, Saudi Arabia 4. Department of Applied Mathematics and Informatics, Technical University, Letná 9, 042 00 Ko(s)ice, Slovakia |
| Abstract: | 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 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. It is natural to ask for the characterization of regular graphs with constant metric dimension. |
| Keywords: | metric dimension basis resolving set cubic graph flower snark convexpolytope |
| 本文献已被 CNKI 维普 万方数据 ScienceDirect 等数据库收录！ | |