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On consecutive edge magic total labelings of connected bipartite graphs

Author

Listed:
  • Bumtle Kang

    (Seoul National University)

  • Suh-Ryung Kim

    (Seoul National University)

  • Ji Yeon Park

    (Kyung Hee University)

Abstract

Since Sedlá $$\breve{\hbox {c}}$$ c ˘ ek introduced the notion of magic labeling of a graph in 1963, a variety of magic labelings of a graph have been defined and studied. In this paper, we study consecutive edge magic labelings of a connected bipartite graph. We make a useful observation that there are only four possible values of b for which a connected bipartite graph has a b-edge consecutive magic labeling. On the basis of this fundamental result, we deduce various interesting results on consecutive edge magic labelings of bipartite graphs. As a matter of fact, we do not focus just on specific classes of graphs, but also discuss the more general classes of non-bipartite and bipartite graphs.

Suggested Citation

  • Bumtle Kang & Suh-Ryung Kim & Ji Yeon Park, 2017. "On consecutive edge magic total labelings of connected bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 13-27, January.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9928-0
    DOI: 10.1007/s10878-015-9928-0
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