A Note on L(2, 1)-labelling of Trees
An L(2, 1)-labelling 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)│≥2 if dG(u, v) = 1 and │f(u) - f(v)│ ≥ 1 if dG(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by A(G), such that there exists an L(...
Saved in:
Published in | 应用数学学报:英文版 Vol. 28; no. 2; pp. 395 - 400 |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
2012
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | An L(2, 1)-labelling 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)│≥2 if dG(u, v) = 1 and │f(u) - f(v)│ ≥ 1 if dG(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by A(G), such that there exists an L(2, 1)-labelling function with no label greater than it. In this paper, we study this problem for trees. Our results improve the result of Wang [The L(2, 1)-labelling of trees, Discrete Appl. Math. 154 (2006) 598-603]. |
---|---|
Bibliography: | An L(2, 1)-labelling 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)│≥2 if dG(u, v) = 1 and │f(u) - f(v)│ ≥ 1 if dG(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by A(G), such that there exists an L(2, 1)-labelling function with no label greater than it. In this paper, we study this problem for trees. Our results improve the result of Wang [The L(2, 1)-labelling of trees, Discrete Appl. Math. 154 (2006) 598-603]. distance-two labelling; L(2, 1)-labelling; tree 11-2041/O1 |
ISSN: | 0168-9673 1618-3932 |