Geodesic
Connected resolvability of graphs
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 827-840.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For an ordered set $W=\lbrace w_1, w_2, \dots , w_k\rbrace $ of vertices and a vertex $v$ in a connected graph $G$, the representation of $v$ with respect to $W$ is the $k$-vector $r(v|W)$ = ($d(v, w_1)$, $d(v, w_2),\dots ,d(v, w_k))$, where $d(x,y)$ represents the distance between the vertices $x$ and $y$. The set $W$ is a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. A resolving set for $G$ containing a minimum number of vertices is a basis for $G$. The dimension $\dim (G)$ is the number of vertices in a basis for $G$. A resolving set $W$ of $G$ is connected if the subgraph $$
Classification : 05C12, 05C25, 05C35
Keywords: resolving set; basis; dimension; connected resolving set; connected resolving number 
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     title = {Connected resolvability of graphs},
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Saenpholphat, Varaporn; Zhang, Ping. Connected resolvability of graphs. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 827-840. http://geodesic.mathdoc.fr/item/CMJ_2003__53_4_a4/