Study on Generator Graphs (K3) of Its Cyclic Groups

The present paper focuses on the connection between the cyclic groups and graphs with cycles especially containing K3 graphs. The study becomes far more interesting if the finite groups are represented in the form of graphs. We established few results on the number of K3 graphs in a cyclic group with respect to the generators that are generating the cyclic groups. The motivation is to transform the generator graph into a fuzzy graph and to find the size and order of the fuzzy generator graph. We proved the results depending on the order of different cyclic groups.