Study on Generator Graphs (K\(_3\)) of Its Cyclic Groups

Abstract

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.