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A group distance magic labeling of a graph G(V, E) with |V | = n is an injection from V to an abelian group Γ of order n such that the sum of labels of all neighbors of every vertex x ∈ V is equal to the same element µ ∈ Γ. We completely characterize all Cartesian products C k 2C m that admit a group distance magic labeling by Z km .
8 We give two results on domination in graphs, including a proof of a conjecture of Favaron, Henning, Mynhart and Puech . Corollary 2 was found by four separate subsets of the authors. We decided to give this joint presentation of our results. We first offer a result about bipartite graphs. Lemma 1 Let G be a bipartite graph with partite sets (X, Y)… (More)
All values of n for which there exist a selfcomplementary circulant graph of order n are determined. Let G be a finite , simple , undirected graph. The graph G is selfcompletementary if G is isomorphic to its complement G ; in symbols , G Ӎ G . It is well known that a selfcomplementary graph of order n exists if f n ϵ 0 or 1 (mod 4). Moreover , a regular… (More)
It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bi-partite graph K n,n with a perfect matching removed can be covered by k bicliques, then n ≤ k k 2. We give a slightly simplified proof and we show that the result is tight. Moreover we use the result to prove analogous bounds for coverings of some other classes of graphs by… (More)
We examine decompositions of complete graphs with an even number of vertices, K 2n , into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings… (More)
The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner's Theorem, the strong isometric dimension of the Hamming graphs K 2 K n is determined.