Some Properties of the Max. Graph for Certain Finite Cyclic Groups
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Abstract
This paper introduces and investigates the Max. graph associated with certain finite cyclic groups. Let G represent a finite cyclic group. The Max. graph for , represent by , that vertex set , and two different vertices and are called adjacent, denoted by , if and only if Max In this case, (x) and (y) represent orders of the elements x and y, respectively, while (G) represents the order of the group G. The simple case and the non-simple case with loops are considered. Explicit formulas are established for the cardinalities of the vertex classes, vertex degrees, and graph size for and . Connectivity, completeness, eccentricity, diameter, radius, center, peripheral vertices, Hamiltonicity, and Eulerianity are also determined. The results show that the structure of the Max. graph is governed by the elements whose orders are equal to the order of the corresponding cyclic group.
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