A search game on the union of graphs with immobile hider

We consider a search game for an immobile hider on one arc of the union of n graphs joined at one or two points. We evaluate a lower bound on the value of a strategy for the hider on this union. When we have identical graphs, we give the conditions under which the value of the strategy for the hider on this union is greater than or equal to n times the value of this strategy on one graph. We also solve search games on graphs, consisting of an odd number of arcs, each of length one, joining two points.