Generalized Euler Function Graphs
Abstract
Let and be positive integers and . For a positive divisor of , we define the generalized Euler function graph of type to be the graph whose vertex set is the set of integers in where the greatest common divisor of and is , and two vertices and are adjacent if and only if the greatest common divisor of and is . The generalized Euler function graph of type is the Euler function graph which has already been studied. In this research, we focus on studying the generalized Euler function graphs of types and . We explore properties of vertices, degree and connectivity of the graphs. Moreover, we present relationships among those graphs, relatively prime graphs and Eulerian graphs.
Keywords : greatest common divisor ; relatively prime graph ; divisor graph
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