| Summary: | A direct product graph is a graph that is formed from the direct product of two different graphs for two groups G and H, labelled as GG and GH. Suppose x1 and y1 be the elements in GG and, x2 and y2 be the elements in GH. Then, two vertices (x1, x2) and (y1, y2) are connected if x1 and y1 are connected in GG, and x2 and y2 are connected in GH. In this research, a new type of graph is introduced and constructed, namely the pi-Cayley graph. This graph is constructed for the symmetric group of order 24 and alternating group of order 12. The graphs obtained are the regular graphs. Then, the direct product of the graphs obtained is also found.
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