The local metric dimension of subgraph-amalgamation of graphs
| Autor: | Barragan-Ramirez, Gabriel A., Simanjuntak, Rinovia, Saputro, Suhadi W., Uttunggadewa, Saladin |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | A vertex $v$ is said to distinguish two other vertices $x$ and $y$ of a nontrivial connected graph G if the distance from $v$ to $x$ is different from the distance from $v$ to $y$. A set $S\subseteq V(G)$ is a local metric set for $G$ if every two adjacent vertices of $G$ are distinguished by some vertex of $S$. A local metric set with minimum cardinality is called a local metric basis for $G$ and its cardinality, the local metric dimension of $G$, denoted by $\dim_l(G)$. In this paper we present tight bounds for the local metric dimension of subgraph-amalgamation of graphs with special emphasis in the case of subgraphs which are isometric embeddings. Comment: 18 pages, 13th Cologne-Twente Workshop on Graphs & Combinatorial Optimization, Istanbul, Turkey May 26-28, 2015 |
| Databáze: | arXiv |
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