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引用次数: 0
摘要
如果满足 G[S] 是 G 的子图且每个顶点 v∈V(G)∖S 有 j≤∣N(v)∩S∣≤k，其中 j 和 k 为非负整数，则图 G 中的一个集合 S⊆V(G) 是 [j, k]-set 。本文主要研究树中 γ(T)-set 和 γ[1,2](T)-set 的情况，并分析了一种称为 spider 的特殊树。然后讨论计算树中[1,2]-域数γ[1,2](T)的两种不同算法。最后，比较并分析计算结果。
The [1,2]-set properties and algorithm analysis of tree
A set S⊆V(G) in graph G is a [j, k]-set if it satisfies that G[S] is a subgraph of G and each vertex v∈V(G)∖S, has j≤∣N(v)∩S∣≤k, wherein j and k are nonnegative integers. In this paper, we focus on the situation of j=1, k=2, that is, [1,2]-set of graph G. We mainly study the situation of γ(T)-set and γ[1,2](T)-set in tree, and analyse a particular tree called spider. Then discuss with two different algorithm to calculate the [1,2]-domination number γ[1,2](T) in tree. Finally, compare and analyze the calculation results.
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