منابع مشابه
Real Number Graph Labellings with Distance Conditions
The theory of integer λ-labellings of a graph, introduced by Griggs and Yeh, seeks to model efficient channel assignments for a network of transmitters. To prevent interference, labels for nearby vertices must be separated by specified amounts ki depending on the distance i, 1 ≤ i ≤ p. Here we expand the model to allow real number labels and separations. The main finding (“D-set Theorem”) is th...
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This paper establishes connections between the structure of a semigroup and the minimum spans of distance labellings of its Cayley graphs. We show that certain general restrictions on the minimum spans are equivalent to the semigroup being combinatorial, and that other restrictions are equivalent to the semigroup being a right zero band. We obtain a description of the structure of all semigroup...
متن کاملDistance-two labellings of Hamming graphs
Let j ≥ k ≥ 0 be integers. An `-L(j, k)-labelling of a graph G = (V , E) is a mapping φ : V → {0, 1, 2, . . . , `} such that |φ(u)−φ(v)| ≥ j if u, v are adjacent and |φ(u)−φ(v)| ≥ k if they are distance two apart. Let λj,k(G) be the smallest integer ` such that G admits an `-L(j, k)-labelling. Define λj,k(G) to be the smallest ` if G admits an `-L(j, k)-labelling with φ(V ) = {0, 1, 2, . . . , ...
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Girth pairs were introduced by Harary and Kovács [Regular graphs with given girth pair, J. Graph Theory 7 (1983) 209–218]. The odd girth (even girth) of a graph is the length of a shortest odd (even) cycle. Let g denote the smaller of the odd and even girths, and let h denote the larger. Then (g, h) is called the girth pair of the graph. In this paper we prove that a graph with girth pair (g, h...
متن کاملThe Edge Span of Distance Two Labellings of Graphs
The radio channel assignment problem can be cast as a graph coloring problem. Vertices correspond to transmitter locations and their labels (colors) to radio channels. The assignment of frequencies to each transmitter (vertex) must avoid interference which depends on the seperation each pair of vertices has. Two levels of interference are assumed in the problem we are concerned. Based on this c...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 1989
ISSN: 0895-4801,1095-7146
DOI: 10.1137/0402044