Labeling trees with a condition at distance two
نویسندگان
چکیده
منابع مشابه
Labeling trees with a condition at distance two
An L(h, k)-labeling of a graph G is an integer labeling of vertices of G, such that adjacent vertices have labels which differ by at least h, and vertices at distance two have labels which differ by at least k. The span of an L(h, k)-labeling is the difference between the largest and the smallest label. We investigate L(h, k)-labelings of trees of maximum degree ∆, seeking those with small span...
متن کاملLabeling planar graphs with a condition at distance two
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic. E-mail: [email protected]. Department of AppliedMathematics, Faculty of Mathematics and Physics, Charles University, Malostranské náměstı́ 25, 118 00 Prague, Czech Republic. E-mail: [email protected]. Institute for Mathematics, Technical University B...
متن کاملLabeling graphs with a condition at distance two
The problem arises from the channel assignment problem. An L(2, 1)-labeling of a graph G = (V,E) is a function f : V → {0, 1, 2, . . .} such that |f(x) − f(y)| ≤ 2 if d(x, y) = 2 and |f(x) − f(y)| ≤ 1 if d(x, y) = 2. The span of an L(2, 1)-labeling is the maximum value f(x) among all vertices x in V . The L(2, 1)-labeling number of G, denoted by λ(G) is the minimum span of an L(2, 1)-labeling. ...
متن کاملA survey on labeling graphs with a condition at distance two
An L(2, 1)-labeling of a graph G = (V,E) is a function f : V → {0, 1, 2, . . .} such that |f(x)− f(y)| ≤ 2 if d(x, y) = 2 and |f(x)− f(y)| ≤ 1 if d(x, y) = 2. The span of an L(2, 1)-labeling is the maximum value f(x) among all vertices x in V . The L(2, 1)labeling number of G, denoted by λ(G) is the minimum span of an L(2, 1)-labeling. A more general setting is as follows. For positive integers...
متن کاملLabeling Dot-Cartesian and Dot-Lexicographic Product Graphs with a Condition at Distance Two
If d(x, y) denotes the distance between vertices x and y in a graph G, then an L(2, 1)-labeling of a graph G is a function f from vertices of G to nonnegative integers such that |f(x)−f(y)| ≥ 2 if d(x, y) = 1, and |f(x)−f(y)| ≥ 1 if d(x, y) = 2. Griggs and Yeh conjectured that for any graph with maximum degree ∆ ≥ 2, there is an L(2, 1)-labeling with all labels not greater than ∆. We prove that...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00750-1