简单图中l距离控制数的上界

Upper Bounds on the Distance l-Domination Number of a Graph

设图G=(V(G),E(G)),如果D■V(G),且对每一个u∈V(G)-D,都存在u′∈D,使得d(u,u′)≤l,则称D为G的一个l-距离控制集.G中阶数最小的l-距离控制集的顶点数称为G的l-距离控制数,记为γl(G).通过研究图的结构和性质,给出了关于γl(G)不同的上界.

For a gra if for each vertex u ph G = （V（G）, E（G））, a subset D lohtain in V（G） is said to be distance l- domination set in if for each vertex u∈G E V（G）-D, there exists a vertex u′ ∈ D such that d（u, u′）≤l. The minimum cardinality of a distance l- domination set in G is called a distance l- domination number and is denoted by γl （G）. By studying the structures and properties of graphs, we obtain various upper bounds for γl（G）.