Search game on the union of n identical graphs joined at one or two points

The conditions are given under which the value of strategy h on a graph which consists of n identical graphs joined at one or two points, where the hider uses the same strategy h/n on every single graph, is n times greater or equal then the value of strategy h on one graph. This gives the possibility that using the value of the game on one graph, the value on the union of more identical graphs can be obtained.