Generalized Euler Function Graphs
Keywords:
greatest common divisor , relatively prime graph , divisor graphAbstract
Let n and d be positive integers and D(n,d): = . For a positive divisor k of n, we define the generalized Euler function graph of type (n,d,k) to be the graph whose vertex set is the set of integers a in D (n,d) where the greatest common divisor of a and n is k, and two vertices a and b are adjacent if and only if the greatest common divisor of a and b is k. The generalized Euler function graph of type (n, 1,1)is the Euler function graph which has already been studied. In this research, we focus on studying the generalized Euler function graphs of types (n, d, 1) and (n, 1, k). We explore properties of vertices, degree and connectivity of the graphs. Moreover, we present relationships among those graphs, relatively prime graphs and Eulerian graphs.
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