On Some families of Path-related graphs with their edge metric dimension
Locating the origin of diffusion in complex networks is an interesting but challenging task. It is crucial for anticipating and constraining the epidemic risks. Source localization has been considered under many feasible models. In this paper, we study the localization problem in some path-related g...
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Elsevier
2024-12-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X24000181 |
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| author | Lianglin Li Shu Bao Hassan Raza |
| author_facet | Lianglin Li Shu Bao Hassan Raza |
| author_sort | Lianglin Li |
| collection | DOAJ |
| description | Locating the origin of diffusion in complex networks is an interesting but challenging task. It is crucial for anticipating and constraining the epidemic risks. Source localization has been considered under many feasible models. In this paper, we study the localization problem in some path-related graphs and study the edge metric dimension. A subset LE⊆VG is known as an edge metric generator for G if, for any two distinct edges e1,e2∈E, there exists a vertex a⊆LE such that d(e1,a)≠d(e2,a). An edge metric generator that contains the minimum number of vertices is termed an edge metric basis for G, and the number of vertices in such a basis is called the edge metric dimension, denoted by dime(G). An edge metric generator with the fewest vertices is called an edge metric basis for G. The number of vertices in such a basis is the edge metric dimension, represented as dime(G). In this paper, the edge metric dimension of some path-related graphs is computed, namely, the middle graph of path M(Pn) and the splitting graph of path S(Pn). |
| format | Article |
| id | doaj-art-b3528a1368e94bf5a608b73bf75cb5a0 |
| institution | DOAJ |
| issn | 2666-657X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
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| series | Examples and Counterexamples |
| spelling | doaj-art-b3528a1368e94bf5a608b73bf75cb5a02025-08-20T02:52:30ZengElsevierExamples and Counterexamples2666-657X2024-12-01610015210.1016/j.exco.2024.100152On Some families of Path-related graphs with their edge metric dimensionLianglin Li0Shu Bao1Hassan Raza2School of Mathematical Sciences, College of Science and Technology, Wenzhou–Kean University, Wenzhou, 325060, ChinaSchool of Mathematical Sciences, College of Science and Technology, Wenzhou–Kean University, Wenzhou, 325060, ChinaCorresponding author.; School of Mathematical Sciences, College of Science and Technology, Wenzhou–Kean University, Wenzhou, 325060, ChinaLocating the origin of diffusion in complex networks is an interesting but challenging task. It is crucial for anticipating and constraining the epidemic risks. Source localization has been considered under many feasible models. In this paper, we study the localization problem in some path-related graphs and study the edge metric dimension. A subset LE⊆VG is known as an edge metric generator for G if, for any two distinct edges e1,e2∈E, there exists a vertex a⊆LE such that d(e1,a)≠d(e2,a). An edge metric generator that contains the minimum number of vertices is termed an edge metric basis for G, and the number of vertices in such a basis is called the edge metric dimension, denoted by dime(G). An edge metric generator with the fewest vertices is called an edge metric basis for G. The number of vertices in such a basis is the edge metric dimension, represented as dime(G). In this paper, the edge metric dimension of some path-related graphs is computed, namely, the middle graph of path M(Pn) and the splitting graph of path S(Pn).http://www.sciencedirect.com/science/article/pii/S2666657X24000181Edge metric basisEdge metric dimensionMiddle graph of pathSplitting graph of path |
| spellingShingle | Lianglin Li Shu Bao Hassan Raza On Some families of Path-related graphs with their edge metric dimension Examples and Counterexamples Edge metric basis Edge metric dimension Middle graph of path Splitting graph of path |
| title | On Some families of Path-related graphs with their edge metric dimension |
| title_full | On Some families of Path-related graphs with their edge metric dimension |
| title_fullStr | On Some families of Path-related graphs with their edge metric dimension |
| title_full_unstemmed | On Some families of Path-related graphs with their edge metric dimension |
| title_short | On Some families of Path-related graphs with their edge metric dimension |
| title_sort | on some families of path related graphs with their edge metric dimension |
| topic | Edge metric basis Edge metric dimension Middle graph of path Splitting graph of path |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X24000181 |
| work_keys_str_mv | AT lianglinli onsomefamiliesofpathrelatedgraphswiththeiredgemetricdimension AT shubao onsomefamiliesofpathrelatedgraphswiththeiredgemetricdimension AT hassanraza onsomefamiliesofpathrelatedgraphswiththeiredgemetricdimension |