科研之友
微信
新浪微博
Facebook
分享链接
摘要
Suppose G is a graph. Two edges e and e' in G are said to be adjacent if they share a common end vertex, and distance two apart if they are nonadjacent but both are adjacent to a common edge. Let j and k be two positive integers. An L(j,k)-edge-labeling of a graph G is an assignment of nonnegative integers, called labels, to the edges of G such that the difference between labels of any two adjacent edges is at least j, and the difference between labels of any two edges that are distance two apart is at least k. The minimum range of labels over all L(j,k)-edge-labelings of a graph G is called the L(j,k)-edge-labeling number of G, denoted by . Let m, j and k be positive integers. An m-circular-L(j,k)-edge-labeling of a graph G is an assignment f from {0,1,aEuro broken vertical bar,m-1} to the edges of G such that, for any two edges e and e', |f(e)-f(e')| (m) a parts per thousand yenj if e and e' are adjacent, and |f(e)-f(e')| (m) a parts per thousand yenk if e and e' are distance two apart, where |a| (m) =min{a,m-a}. The minimum m such that G has an m-circular-L(j,k)-edge-labeling is called the circular-L(j,k)-edge-labeling number of G, denoted by . This paper investigates the L(1,1)-edge-labeling numbers, the L(2,1)-edge-labeling numbers and the circular-L(2,1)-edge-labeling numbers of the hexagonal lattice, the square lattice, the triangular lattice and the strong product of two infinite paths.
- 出版日期2013-5
- 单位东南大学
