Author(s): Jimly Manuel

Abstract: In this paper, we investigate the structural properties of the undirected power graph (GZ_n) associated with the finite cyclic group Z_n. We begin by establishing the necessary and sufficient conditions under which (GZ_n) It is bipartite and characterizes its clique structure. Explicit formulas are derived for the degree of a vertex based on the subgroup structure of Z_n, leading to a criterion for identifying the minimum degree in the graph. We also analyze distance-related parameters, including radius, diameter, and average distance, and explore conditions under which these attain extremal values. The number of vertex pairs at distance two is computed for specific group orders, such as (GZ_pq) and (GZ_p²_q), revealing intricate combinatorial relationships. These results enhance the understanding of how algebraic properties of Z_n influence the topology of its power graph.

DOI: 10.22271/maths.2025.v10.i8b.2129

Pages: 94-97 | Views: 183 | Downloads: 14

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