一些图运算下的k-角色分配

k-role assignments under some graph operations

给定图G,考虑从其顶点集到角色集{1,2,…,k}的一个满射r。对任意2个具有相同角色的顶点,如果它们邻域所拥有的角色构成的集合相同,则称r为G的一个k-角色分配。对一些图运算下的k-角色分配进行了研究,这些图运算包括联、笛卡尔积、字典式积、弱直积,Mycielski图。

Given graph G,we consider a surjective function r mapping each vertex into a role,a positive integer in {1,2,…,k}.For any two vertices with the same role,if the sets of roles assigned to their neighbors are the same,then we call r a k-role assignment.In this paper we study the k-role assignments under some graph operations including join,cartesian product,lexicographic product,categorical product and Mycielski＇s graphs.