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A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN extensions and free products with amalgamation. Graph products with cyclic edge groups inherit a solvable conjugacy problem from their vertex groups under certain conditions, the most important of which imposed here is that all the edge group generators in each vertex group are powers of a common central element. Under these conditions the conjugacy problem is solvable for any two elements notdoi:10.2307/2045299 fatcat:t4da2bfyqvgqlicaaawnfiwydi