给定最小度图的2-距离控制数的上界

2-Distance Domination in Graphs with Given Minimum Degree

设G=(V,E)为一个简单图.如果对于任意不属于集合S的顶点v,都存在S中一点u,满足u和v之间的距离小于等于k,则称子集S?V为G的一个k-距离控制集.图G的k-距离控制数是指G中最小的k-距离控制集所含元素数目,记作γ_(k)(G).利用Bujtás权转移的方法给出了2-距离控制数的上界的一个简短证明.

Let G=(V,E) be a graph.S?V (G) is called a k-distance-dominating set of G if every vertex of G-S is within distance k from some vertex of S.The smallest cardinality of a k-distance-dominating set of G is the k-distance-dominating number of G,denoted byγ_(k)(G).By using Bujtás discharge method,an short proof is given for the upper bound of 2-distance domination number of a graph with given order and minimum degree.