Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are...Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.展开更多
For a graph G and two positive integers j and k an m-L j k -edge-labeling of G is an assignment from the set 0 1 … m-to the edges such that adjacent edges receive labels that differ by at least j and edges at distanc...For a graph G and two positive integers j and k an m-L j k -edge-labeling of G is an assignment from the set 0 1 … m-to the edges such that adjacent edges receive labels that differ by at least j and edges at distance two receive labels that differ by at least k.Theλ′j k-number of G denoted byλ′j k G is the minimum integer m overall m-L j k -edge-labeling of G.The necklace is a specific type of Halin graph.The L 1 2 -edge-labeling of necklaces is studied and the lower and upper bounds on λ′1 2-number for necklaces are given.Also both the lower and upper bounds are attainable.展开更多
An L（j, k）-labeling of a graph G is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive integers which are at least j apart, and vertices at distance two receive integers w...An L（j, k）-labeling of a graph G is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive integers which are at least j apart, and vertices at distance two receive integers which are at least k apart. Given an L（j, k）-labeling f of G, define the L（j, k） edge span of f, βj,k（G,f） =max{ ｜f（x）-f（y）｜： {x,y}∈E（G）}. The L（j,k） edge span of G, βj,k （G） is min βj,k（ G, f）, where the minimum runs over all L（j, k）-labelings f of G. The real L（.j, k）-labeling of a graph G is a generalization of the L（j, k）-labeling. It is an assignment of nonnegative real numbers to the vertices of G satisfying the same distance one and distance two conditions. The real L（j, k） edge span of a graph G is defined accordingly, and is denoted by βj,k（G）. This paper investigates some properties of the L（j, k） edge span and the real L（j, k） edge span of graphs, and completely determines the edge spans of cycles and complete t-partite graphs.展开更多
基金The National Natural Science Foundation of China(No.10971025)
文摘Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.
基金The National Natural Science Foundation of China(No.10971025,10901035)
文摘For a graph G and two positive integers j and k an m-L j k -edge-labeling of G is an assignment from the set 0 1 … m-to the edges such that adjacent edges receive labels that differ by at least j and edges at distance two receive labels that differ by at least k.Theλ′j k-number of G denoted byλ′j k G is the minimum integer m overall m-L j k -edge-labeling of G.The necklace is a specific type of Halin graph.The L 1 2 -edge-labeling of necklaces is studied and the lower and upper bounds on λ′1 2-number for necklaces are given.Also both the lower and upper bounds are attainable.
基金The National Natural Science Foundation of China (No10971025)
文摘An L（j, k）-labeling of a graph G is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive integers which are at least j apart, and vertices at distance two receive integers which are at least k apart. Given an L（j, k）-labeling f of G, define the L（j, k） edge span of f, βj,k（G,f） =max{ ｜f（x）-f（y）｜： {x,y}∈E（G）}. The L（j,k） edge span of G, βj,k （G） is min βj,k（ G, f）, where the minimum runs over all L（j, k）-labelings f of G. The real L（.j, k）-labeling of a graph G is a generalization of the L（j, k）-labeling. It is an assignment of nonnegative real numbers to the vertices of G satisfying the same distance one and distance two conditions. The real L（j, k） edge span of a graph G is defined accordingly, and is denoted by βj,k（G）. This paper investigates some properties of the L（j, k） edge span and the real L（j, k） edge span of graphs, and completely determines the edge spans of cycles and complete t-partite graphs.
