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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2408.06746 |
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| _version_ | 1866910564753604608 |
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| author | Syofyan, Dian Kastika Saputro, Suhadi Wido Baskoro, Edy Tri Purwasih, Ira Apni |
| author_facet | Syofyan, Dian Kastika Saputro, Suhadi Wido Baskoro, Edy Tri Purwasih, Ira Apni |
| contents | Let $G=(V,E)$ be a finite, simple, and connected graph. The locating-chromatic number of a graph $G$ can be defined as the cardinality of a minimum resolving partition of the vertex set $V(G)$ such that all vertices have different coordinates and every two adjacent vertices in $G$ is not contained in the same partition class. In this case, the coordinate of a vertex in $G$ is expressed in terms of the distances of this vertex to all partition classes. The corona product of a graph $G$ of order $n$ and a graph $H,$ denoted by $G \odot H,$ is the graph obtained by taking one copy of $G$ and $n$ copies of $H$ and joining the $i^{th}$-vertex of $G$ to every vertex in the $i^{th}$-copy of $H$. In this paper, we determine the sharp general bound of the locating-chromatic number of $G \odot H$ for $G$ is a connected graph and $H$ is an arbitrary graph, or $G$ is a tree graph and $H$ is a complement of complete graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the locating-chromatic number of corona product of graphs Syofyan, Dian Kastika Saputro, Suhadi Wido Baskoro, Edy Tri Purwasih, Ira Apni Combinatorics 05C12 Let $G=(V,E)$ be a finite, simple, and connected graph. The locating-chromatic number of a graph $G$ can be defined as the cardinality of a minimum resolving partition of the vertex set $V(G)$ such that all vertices have different coordinates and every two adjacent vertices in $G$ is not contained in the same partition class. In this case, the coordinate of a vertex in $G$ is expressed in terms of the distances of this vertex to all partition classes. The corona product of a graph $G$ of order $n$ and a graph $H,$ denoted by $G \odot H,$ is the graph obtained by taking one copy of $G$ and $n$ copies of $H$ and joining the $i^{th}$-vertex of $G$ to every vertex in the $i^{th}$-copy of $H$. In this paper, we determine the sharp general bound of the locating-chromatic number of $G \odot H$ for $G$ is a connected graph and $H$ is an arbitrary graph, or $G$ is a tree graph and $H$ is a complement of complete graph. |
| title | On the locating-chromatic number of corona product of graphs |
| topic | Combinatorics 05C12 |
| url | https://arxiv.org/abs/2408.06746 |