TY - JOUR
T1 - A note on L(2, 1)-labelling of trees
AU - Zhai, Ming Qing
AU - Lu, Chang Hong
AU - Shu, Jin Long
PY - 2012/5
Y1 - 2012/5
N2 - 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 {pipe}f(u) - f(v){pipe} ≥ 2 if d G(u, v) = 1 and {pipe}f(u) - f(v){pipe} ≥ 1 if d G(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by λ(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].
AB - 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 {pipe}f(u) - f(v){pipe} ≥ 2 if d G(u, v) = 1 and {pipe}f(u) - f(v){pipe} ≥ 1 if d G(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by λ(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].
KW - L(2, 1)-labelling
KW - distance-two labelling
KW - tree
UR - https://www.scopus.com/pages/publications/84860489485
U2 - 10.1007/s10255-012-0151-9
DO - 10.1007/s10255-012-0151-9
M3 - 文章
AN - SCOPUS:84860489485
SN - 0168-9673
VL - 28
SP - 395
EP - 400
JO - Acta Mathematicae Applicatae Sinica
JF - Acta Mathematicae Applicatae Sinica
IS - 2
ER -