Rainbow vertex-connection and graph products.

A vertex-coloured graphGis said to berainbow vertex-connectedif every two vertices ofGare connected by a path whose internal vertices have distinct colours, such a path is called a rainbow path. Therainbow vertex-connection numberof a connected graphG, denoted by, is the smallest number of colours that are needed in order to makeGrainbow vertex-connected. In this paper, we study the rainbow vertex-connection number on the lexicographical, strong, Cartesian and direct product and present several upper bounds for these products of graphs. The rainbow vertex-connection number of some product networks is also investigated in this paper. [ABSTRACT FROM AUTHOR]