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Some Resolving Parameters in a Class of Cayley Graphs

Authors :
Jia-Bao Liu
Ali Zafari
Source :
Journal of Mathematics, Vol 2022 (2022)
Publication Year :
2022
Publisher :
Hindawi, 2022.

Abstract

Resolving parameters is a fundamental area of combinatorics with applications not only to many branches of combinatorics but also to other sciences. In this article, we construct a class of Toeplitz graphs, and will be denoted by $T_{2n}(W)$, so that they are Cayley graphs. First, we review some of the features of this class of graphs. In fact, this class of graphs are vertex transitive, and by calculating the spectrum of the adjacency matrix related with them, we show that this class of graphs cannot be edge transitive. Moreover, we show that this class of graphs cannot be distance regular, and since the computing resolving parameters of a class of graphs such that are not distance regular is more difficult, then we regard this as justification for our focus on some resolving parameters. In particular, we determine the minimal resolving set, doubly resolving set and strong metric dimension for this class of graphs.<br />Comment: arXiv admin note: substantial text overlap with arXiv:1905.10527

Details

Language :
English
ISSN :
23144629
Database :
OpenAIRE
Journal :
Journal of Mathematics
Accession number :
edsair.doi.dedup.....3dfa4b19ea180ed0ac733d0b6a386c1d
Full Text :
https://doi.org/10.1155/2022/9444579