A Note On Graphs Representable As Product Graphs
A theorem is proved which implies affirmative answers to the problems of E. Prisner. One problem is whether there are cycles of the line graph operator with period other than 1, the other whether there are cycles of the 4-edge graph operator with period greater than 2. Then a similar theorem follows.
In this version of the Cops and Robber game, the cops move in tandems, or pairs, such that they are at distance at most one from each other after every move. The problem is to determine, for a given graph G, the minimum number of tandems sufficient to guarantee a win for the cops. We investigate this game on three graph products, the Cartesian, categorical and strong products.