# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# The metric dimension of $n$-complete partite graph minus perfect matching

Presented by Mr. Suhadi Wido SAPUTRO
Type: Oral presentation
Track: General session

## Content

A set of vertices $W$ \textit{resolves} a graph $G$ if every vertex in $G$ is uniquely determined by its vector of distances to the vertices in $W$. \ The \textit{metric dimension }of $G$ is the minimum cardinality of a resolving set of $G$. \ For $n\geq 3$, an $n$-complete partite graph $G(k_1, k_2, ..., k_n)$ is a graph whose vertex set $V$ can be partitioned into $n$ subsets $V_1, V_2, ...,V_n$, with $|V_i|=k_i \geq 3$, such that every edge of $G(k_1, k_2, ..., k_n)$ joins $V_1, V_2, ...,V_n$. \ Recently, we have determined the metric dimension of regular bipartite which is isomorph to a complete bipartite graph minus a perfect matching (Baca \emph{et al.}, Bull. Math. Soc. Sci. Math. Roumanie, $2011$). \ Continuing our previous results, in this paper we determine the metric dimension of $G(k_1, k_2, ..., k_n)$ minus a perfect matching.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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