Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph
Let G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S. The minimal doubly resolving set of vertices of graph...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6267072 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560055003643904 |
|---|---|
| author | Jia-Bao Liu Ali Zafari |
| author_facet | Jia-Bao Liu Ali Zafari |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | Let G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S. The minimal doubly resolving set of vertices of graph G is a doubly resolving set with minimum cardinality and is denoted by ψG. In this paper, first, we construct a class of graphs of order 2n+Σr=1k−2nmr, denoted by LSGn,m,k, and call these graphs as the layer Sun graphs with parameters n, m, and k. Moreover, we compute minimal doubly resolving sets and the strong metric dimension of the layer Sun graph LSGn,m,k and the line graph of the layer Sun graph LSGn,m,k. |
| format | Article |
| id | doaj-art-a87f03e4b07e426b863962d9ec7def1e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a87f03e4b07e426b863962d9ec7def1e2025-02-03T01:28:34ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/62670726267072Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun GraphJia-Bao Liu0Ali Zafari1School of Finance and Mathematics, Huainan Normal University, Huainan 232038, ChinaDepartment of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-4697, Tehran, IranLet G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S. The minimal doubly resolving set of vertices of graph G is a doubly resolving set with minimum cardinality and is denoted by ψG. In this paper, first, we construct a class of graphs of order 2n+Σr=1k−2nmr, denoted by LSGn,m,k, and call these graphs as the layer Sun graphs with parameters n, m, and k. Moreover, we compute minimal doubly resolving sets and the strong metric dimension of the layer Sun graph LSGn,m,k and the line graph of the layer Sun graph LSGn,m,k.http://dx.doi.org/10.1155/2020/6267072 |
| spellingShingle | Jia-Bao Liu Ali Zafari Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph Complexity |
| title | Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph |
| title_full | Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph |
| title_fullStr | Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph |
| title_full_unstemmed | Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph |
| title_short | Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph |
| title_sort | computing minimal doubly resolving sets and the strong metric dimension of the layer sun graph and the line graph of the layer sun graph |
| url | http://dx.doi.org/10.1155/2020/6267072 |
| work_keys_str_mv | AT jiabaoliu computingminimaldoublyresolvingsetsandthestrongmetricdimensionofthelayersungraphandthelinegraphofthelayersungraph AT alizafari computingminimaldoublyresolvingsetsandthestrongmetricdimensionofthelayersungraphandthelinegraphofthelayersungraph |