Antimagic Labelings of Join Graphs

详细信息    查看全文

• 作者：Martin Ba?a ; Oudone Phanalasy ; Joe Ryan…
• 关键词：Antimagic labeling ; Join graph ; Complete multipartite graph ; Primary 05C78
• 刊名：Mathematics in Computer Science
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：9
• 期：2
• 页码：139-143
• 全文大小：384 KB
• 参考文献：1.Alon N., Kaplan G., Lev A., Roditty Y., Yuster R.: Dense graphs are antimagic. J. Graph Theory 47(4), 297-09 (2004)MATH MathSciNet View Article
  2.Ba?a M., Miller M.: Super Edge-Antimagic Graphs: A Wealth of Problems and Some Solutions. BrownWalker Press, Boca Raton (2008)
  3.Ba?a M., Miller M., Phanalasy O., Semani?ová-Feňov?íková A.: Constructions of antimagic labelings for some families of regular graphs. J. Algorithms Comput. 44, 1- (2013)
  4.Cheng Y.: A new class of antimagic Cartesian product graphs. Discrete Math. 308(24), 6441-448 (2008)MATH MathSciNet View Article
  5.Cranston D.W.: Regular bipartite graphs are antimagic. J. Graph Theory 60(3), 173-82 (2009)MATH MathSciNet View Article
  6.Gallian, J.A.: A dynamic survey of graph labeling. Electron. J. Combin. 17(\({\sharp}\) DS6) (2014)
  7.Hartsfield N., Ringel G.: Pearls in Graph Theory: A Comprehensive Introduction. Academic Press Inc., Boston (1990)MATH
  8.Phanalasy O., Miller M., Rylands L.J., Lieby P.: On a relationship between completely separating systems and antimagic labeling of regular graphs. LNCS 6460, 238-41 (2011)MathSciNet
  9.Rylands L., Phanalasy O., Ryan J., Miller M.: An application of completely separating systems to graph labeling. LNCS 8288, 376-87 (2013)MathSciNet
  10.Wang T.M., Hsiao C.C.: On anti-magic labeling for graph products. Discrete Math. 308(16), 3624-633 (2008)MATH MathSciNet View Article
  11.Zhang Y., Sun X.: The antimagicness of the Cartesian product of graphs. Theor. Comput. Sci. 410, 727-35 (2009)MATH View Article
  
• 作者单位：Martin Ba?a (1)
  Oudone Phanalasy (2) (3)
  Joe Ryan (4)
  Andrea Semani?ová-Feňov?íková (1)
  
  1. Department of Applied Mathematics and Informatics, Technical University, Ko?ice, Slovakia
  2. School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, Australia
  3. Department of Mathematics, National University of Laos, Vientiane, Laos
  4. School of Electrical Engineering and Computer Science, University of Newcastle, Newcastle, Australia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Computer Science, general
  
• 出版者：Springer Basel
• ISSN：1661-8289

文摘

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.