Labeling Dot-Cartesian and Dot-Lexicographic Product Graphs with a Condition at Distance Two
نویسندگان
چکیده
منابع مشابه
Labeling 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...
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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...
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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. ...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 2015
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/bxv084