The generalized Kautz digraphs have many good properties as interconnection network topologies. In this note, the bounds of the absorbant number for the generalized Kautz digraph are given, and some sufficient conditi...The generalized Kautz digraphs have many good properties as interconnection network topologies. In this note, the bounds of the absorbant number for the generalized Kautz digraph are given, and some sufficient conditions for the absorbant number of the generalized Kautz digraph attaining the bounds are presented.展开更多
Let G = (V,A) be a digraph.A set T of vertices of G is a twin dominating set of G if for every vertex v ∈ V / T.There exist u,w ∈ T (possibly u = w) such that (u,v),(v,w) ∈ A.The twin domination number γ...Let G = (V,A) be a digraph.A set T of vertices of G is a twin dominating set of G if for every vertex v ∈ V / T.There exist u,w ∈ T (possibly u = w) such that (u,v),(v,w) ∈ A.The twin domination number γ*(G) of G is the cardinality of a minimum twin dominating set of G.In this paper we consider the twin domination number in generalized Kautz digraphs GK(n,d).In these digraphs,we establish bounds on the twin domination number and give a sufficient condition for the twin domination number attaining the lower bound.We give the exact values of the twin domination numbers by constructing minimum twin dominating sets for some special generalized Kautz digraphs.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.10571117,60773078)Shu Guang Plan of Shanghai Education Development Foundation (Grant No.06SG42)the Shanghai Leading Academic Discipline Project(Grant No.J50101)
文摘The generalized Kautz digraphs have many good properties as interconnection network topologies. In this note, the bounds of the absorbant number for the generalized Kautz digraph are given, and some sufficient conditions for the absorbant number of the generalized Kautz digraph attaining the bounds are presented.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10571117, 60773078)the Shuguang Plan of Shanghai Education Development Foundation (Grant No.06SG42)the Shanghai Leading Academic Discipline Project(Grant No.J50101)
文摘Let G = (V,A) be a digraph.A set T of vertices of G is a twin dominating set of G if for every vertex v ∈ V / T.There exist u,w ∈ T (possibly u = w) such that (u,v),(v,w) ∈ A.The twin domination number γ*(G) of G is the cardinality of a minimum twin dominating set of G.In this paper we consider the twin domination number in generalized Kautz digraphs GK(n,d).In these digraphs,we establish bounds on the twin domination number and give a sufficient condition for the twin domination number attaining the lower bound.We give the exact values of the twin domination numbers by constructing minimum twin dominating sets for some special generalized Kautz digraphs.