The [1,2]-set properties and algorithm analysis of tree

Abstract

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.