The Domination Number of K 3 n
Let K3n denote the Cartesian product Kn□Kn□Kn, where Kn is the complete graph on n vertices. We show that the domination number of K3n is [...]
Vertex rainbow colorings of graphs
In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P. If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a vertex rainbow coloring of G. The minimum number of colors needed in a vertex rainbow coloring of G is the vertex rainbow connection number vrc(G) of...
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