Digraph from power mapping on noncommutative groups



报告题目:Digraph from power mapping on noncommutative groups



报告摘要:Let X be a group and k be a positive integer. The k-power digraph G(X, k) is consisting of vertex set X and there is a directed edge from x to y if and only if x^k = y. We study the k-power digraph on the semiproduct of cyclic groups. In particular, we obtain the distribution of indegree and cycles, and determine the structure of trees attached with vertices of power digraph. Finally, we establish a necessary and sufficient ccondition for isomorphism of digraphs G(X, k1) and G(X, k2).