A Cayley graph is a graph of a group that is build based on a specific subset of the group. The vertices of the graph are the elements of the group, and two different vertices, x and y are adjacent if the product of x and inverse of y is in the subset. One type of Cayley graph recently introduced is the prime power Cayley graph in which the subset of the group considered in constructing this graph contains the elements dividing the order of the group. In this paper, we construct all possible prime power Cayley graphs based on the subsets for the cyclic group of order pq where p and q are primes. The results show that there are seven possible prime power Cayley graphs for this group.

Topics
Graph theory
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