Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v...Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.展开更多
An L（d0,d2,...,dt）-labeling of a graph G is a function f from its vertex set V（G） to the set {0,1,..., k} for some positive integer k such that If（x） - f（y）l ≥di, if the distance between vertices x and y in G...An L（d0,d2,...,dt）-labeling of a graph G is a function f from its vertex set V（G） to the set {0,1,..., k} for some positive integer k such that If（x） - f（y）l ≥di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L（d1,d2,...,dt）-number λ（G;d1,d2,... ,dt） of G is the smallest integer number k such that G has an L（d1,d2,...,dr）- labeling with max{f （x）｜x ∈ V（G）} = k. In this paper, we obtain the exact values for λ（Cn; 2, 2, 1） and λ（Cn; 3, 2, 1）, and present lower and upper bounds for λ（Cn; 2,..., 2, 1,..., 1）展开更多
文摘Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.
基金the National Natural Science Foundation of China (No.10531070)the National Basic Research Program of China 973 Program (No.2006AA11Z209)the Natural Science Foundation of Shanghai City (No.06ZR14049)
文摘An L（d0,d2,...,dt）-labeling of a graph G is a function f from its vertex set V（G） to the set {0,1,..., k} for some positive integer k such that If（x） - f（y）l ≥di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L（d1,d2,...,dt）-number λ（G;d1,d2,... ,dt） of G is the smallest integer number k such that G has an L（d1,d2,...,dr）- labeling with max{f （x）｜x ∈ V（G）} = k. In this paper, we obtain the exact values for λ（Cn; 2, 2, 1） and λ（Cn; 3, 2, 1）, and present lower and upper bounds for λ（Cn; 2,..., 2, 1,..., 1）
