Abstract
A graph consists of points which are called vertices, and connections which are called edges, which are indicated by line segments or curves joining certain pairs of vertices. In this paper, four types of graphs which are the commuting graph, non-commuting graph conjugate graph and the conjugacy class graph for some three-generator groups are discussed. Some of the graph properties are also found which include the independent number, chromatic number, clique number and dominating number.
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