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Oudone Phanalasy Mirka Miller Costas S. Iliopoulos Solon P. Pissis Elaheh Vaezpour 《Mathematics in Computer Science》2011,5(1):81-87
An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, . . . , q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with
the vertex. A graph is antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that that every
connected graph, except K
2, is antimagic. Recently, using completely separating systems, Phanalasy et al. showed that for each
k 3 2, q 3 \binomk+12{k\geq 2,\,q\geq\binom{k+1}{2}} with k|2q, there exists an antimagic k-regular graph with q edges and p = 2q/k vertices. In this paper we prove constructively that certain families of Cartesian products of regular graphs are antimagic. 相似文献
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An antimagic labeling of a graph withq edges is a bijection from the set of edges to the set of positive integers{1,2,...,q}such that all vertex weights are pairwise distinct,where the vertex weight of a vertex is the sum of the labels of all edges incident with that vertex.A graph is antimagic if it has an antimagic labeling.In this paper,we provide antimagic labelings for a family of generalized pyramid graphs. 相似文献
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Martin?Ba?a Oudone?PhanalasyEmail author Joe?Ryan Andrea?Semani?ová-Feňov?íková 《Mathematics in Computer Science》2015,9(2):139-143
An antimagic labeling of a graph with q edges is a bijection from the set of edges of the graph to the set of positive integers \({\{1, 2,\dots,q\}}\) such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. The join graph G + H of the graphs G and H is the graph with \({V(G + H) = V(G) \cup V(H)}\) and \({E(G + H) = E(G) \cup E(H) \cup \{uv : u \in V(G) {\rm and} v \in V(H)\}}\). The complete bipartite graph K m,n is an example of join graphs and we give an antimagic labeling for \({K_{m,n}, n \geq 2m + 1}\). In this paper we also provide constructions of antimagic labelings of some complete multipartite graphs. 相似文献
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Martin Bača Mirka Miller Oudone Phanalasy Andrea Semaničová-Feňovčíková 《数学学报(英文版)》2010,26(12):2283-2294
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face, and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s that appears in the graph. The paper examines the existence of such labelings for disjoint union of plane graphs. 相似文献
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