An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u...An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.展开更多
Given two non-negative integers h and k, an L（h, k）-labeling of a graph G = （V, E） is a function from the set V to a set of colors, such that adjacent nodes take colors at distance at least h, and nodes at distanc...Given two non-negative integers h and k, an L（h, k）-labeling of a graph G = （V, E） is a function from the set V to a set of colors, such that adjacent nodes take colors at distance at least h, and nodes at distance 2 take colors at distance at least k. The aim of the L（h, k）-labeling problem is to minimize the greatest used color. Since the decisional version of this problem is NP-complete, it is important to investigate particular classes of graphs for which the problem can be efficiently solved. It is well known that the most common interconnection topologies, such as Butterfly-like, Beneg, CCC, Trivalent Cayley networks, are all characterized by a similar structure： they have nodes organized as a matrix and connections are divided into layers. So we naturally introduce a new class of graphs, called （l × n）-multistage graphs, containing the most common interconnection topologies, on which we study the L（h, k）-labeling. A general algorithm for L（h, k）-labeling these graphs is presented, and from this method an efficient L（2, 1）-labeling for Butterfly and CCC networks is derived. Finally we describe a possible generalization of our approach.展开更多
基金Supported by the Natural Science Foundation of Education Ministry of Anhui Province (No.KJ2010B138)the Foundation for the Excellent Young Talents of Anhui Province(No.2010SQRL136ZD)the Natural Science Foundation of Chuzhou University(No.2008kj013B)
基金The NSF (60673048) of China the NSF (KJ2009B002,KJ2009B237Z) of Education Ministry of Anhui Province.
文摘An L（3, 2, 1）-labeling of a graph G is a function from the vertex set V（G） to the set of all nonnegative integers such that ｜f（u）-f（v）｜≥3 if dG（u,v） = 1, ｜f（u）-f（v）｜≥2 if dG（u,v） = 2, and ｜f（u）-f（v）｜≥1 if dG（u,v） = 3. The L（3, 2,1）-labeling problem is to find the smallest number λ3（G） such that there exists an L（3, 2,1）-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3（T） attains the minimum value.
基金National Natural Science Foundation of China(No.10671074 and No.60673048)Natural Science Foundation of Education Ministry of Anhui Province(No.KJ2007B124 and No.2006KJ256B)
基金Sapienza University of Rome(project"Parallel and Distributed Codes")
文摘Given two non-negative integers h and k, an L（h, k）-labeling of a graph G = （V, E） is a function from the set V to a set of colors, such that adjacent nodes take colors at distance at least h, and nodes at distance 2 take colors at distance at least k. The aim of the L（h, k）-labeling problem is to minimize the greatest used color. Since the decisional version of this problem is NP-complete, it is important to investigate particular classes of graphs for which the problem can be efficiently solved. It is well known that the most common interconnection topologies, such as Butterfly-like, Beneg, CCC, Trivalent Cayley networks, are all characterized by a similar structure： they have nodes organized as a matrix and connections are divided into layers. So we naturally introduce a new class of graphs, called （l × n）-multistage graphs, containing the most common interconnection topologies, on which we study the L（h, k）-labeling. A general algorithm for L（h, k）-labeling these graphs is presented, and from this method an efficient L（2, 1）-labeling for Butterfly and CCC networks is derived. Finally we describe a possible generalization of our approach.
