Connectivity of Power Graphs of Cyclic Groups with Specific Orders
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Abstract
The power graph is defined as a graph whose vertexset consists of the elements of a group, where two vertices arejoined by an edge if one element is a power of the other. In thisresearch we discuss the power graph of a cyclic group of order n=pq, with p and q distinct prime numbers, illustrates theconnectivity among its vertices and reveals important topologicalproperties such as the diameter and the clique number. Fur-thermore, this study also examines the degrees of the verticesand provides an analysis of the Hamiltonian, Eulerian, andplanar characteristics of the graph. These findings highlighthow algebraic structures can be effectively explored throughgraph-theoretical perspectives, offering deeper insights into theinterplay between group theory and graph topology.
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