Super d-anti-magic labeling of subdivided kC5

Super d-anti-magic labeling of subdivided kC5

A graph (G = (V, E, F)) admits labeling of type (1, 1, 1) if we assign labels from the set {1, 2, 3, ..., |V (G)| + |E(G)| + |F(G)|} to the vertices, edges, and faces of a planar graph G in such a way that each vertex, edge, and face receives exactly one label and each number is used exactly once as a label and the weight of each face under the mapping is the same. Super d-antimagic labeling of type (1, 1, 1) on snake kC5 , subdivided kC5 as well as ismorphic copies of kC5 for string (1, 1, ..., 1) and string (2, 2, ..., 2) is discussed in this paper.

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  • [1] Baca M. On magic and consecutive labelings for the special classes of plane graphs. Utilitas Mathematica 1987; 32: 59–65.
  • [2] Baca M. On magic labelings of grid graphs. Ars Combinatoria 1992; 33: 295–299.
  • [3] Baca M. On magic labelings of honeycomb. Discrete Math 1992; 105: 305–311.
  • [4] Baca M. On magic labelings of M¨obius ladders. J Franklin Inst 1989; 326: 885–888.
  • [5] Baca M. On magic labelings of type (1,1,1) for three classes of plane graphs. Math Slovaca 1989; 39: 233–239.
  • [6] Baca M. Labelings of m-antiprisms. Ars Combinatoria 1989; 28: 242–245.
  • [7] Baca M. Labelings of two classes of convex polytopes. Utilitas Mathematica 1988; 34: 24–31.
  • [8] Baca M. On magic labelings of m-prisms. Math Slovaca 1990; 40: 11–14.
  • [9] Baca M. Labelings of two classes of plane graphs. Acta Math Appl Sinica 1993; 9: 82–87.
  • [10] Baca M. On magic labelings of type (1,1,1) for the special class of plane graphs. J Franklin Inst 1992; 329: 549–553.
  • [11] Baca M. On magic labelings of convex polytopes. Ann Disc Math 1992; 51: 13–16.
  • [12] Baca M, Holl´ander I. Labelings of a certain class of convex polytopes. J. Franklin Inst 1992; 329: 539–547.
  • [13] Baca M, Numan M, Kashif M. Super face anti labeling of union of antiprism. Mathematics in Computer Science 2013; 7: 245–252.
  • [14] Barientos C. Difference vertex labelings, PhD Thesis, Universitat Po-litecnica De Catalunya. Spain 2004.
  • [15] Siddiqui MK, Numan M, Umar MA. Face Antimagic Labeling of Jahangir Graph. Mathematics in Computer Science 2013: 1–7.
  • [16] Ali K, Hussain M, Ahmed A, Miller M. Magic labelings of type (a,b,c) of families of wheels. Mathematics in Computer in Science 2013; 7: 315–319.
  • [17] Lih KW. On magic and consecutive labelings of plane graphs. Utilitas Mathematica 1983; 24: 165–197.
  • [18] Gallian JA. A dynamic survey of graph labeling. Electron J Comb 2014; 17: DS6.
  • [19] Rosa A. Cyclic steiner triple systems and labelings of triangular cacti. Sci Ser A Math Sci (N. S.) 1998; 1: 87–95.