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On the strong metric dimension of corona product graphs and join graphs
Strong metric dimension strong resolving sets strong metric basis clique number corona graph
2012/4/18
Let $G$ be a connected graph. A vertex $w$ strongly resolves a pair $u$, $v$ of vertices of $G$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A se...
On the metric dimension of line graphs
Metric dimension resolving set line graph de Brujin digraph Kautz digraph
2011/9/16
Abstract: Let $G$ be a (di)graph. A set $W$ of vertices in $G$ is a \emph{resolving set} of $G$ if every vertex $u$ of $G$ is uniquely determined by its vector of distances to all the vertices in $W$....
Krausz dimension and its generalizations in special graph classes
Krausz dimension intersection graphs linear k-uniform hypergraphs chordal graphs polar graphs
2011/9/14
Abstract: A {\it krausz $(k,m)$-partition} of a graph $G$ is the partition of $G$ into cliques, such that any vertex belongs to at most $k$ cliques and any two cliques have at most $m$ vertices in com...
d-Representability of simplicial complexes of fixed dimension
Combinatorics d-Representability fixed dimension
2011/8/26
Abstract: Let K be a simplicial complex with vertex set V = {v_1,..., v_n}. The complex K is d-representable if there is a collection {C_1,...,C_n} of convex sets in R^d such that a subcollection {C_{...
Enumeration of $\C{H}$-strata in quantum matrices with respect to dimension
$\C{H}$-strata in quantum matrices dimension
2010/12/6
We present a combinatorial method to determine the dimension of H-strata in the algebra of m n quantum matrices Oq(Mm;n(K)) as follows. To a given H-stratum we associate a certain permutation via th...