Super d-anti-magic labeling of subdivided $kC_{5}$

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 $kC_{5}$, subdivided $kC_{5}$ as well as ismorphic copies of $kC_{5}$ for string $(1,1,...,1)$ and string $(2,2,...,2)$ is discussed in this paper.

Anahtar Kelimeler:

Super d-anti-magic labeling, snake graph

Super d-anti-magic labeling of subdivided $kC_{5}$

Keywords:

Super d-anti-magic labeling, snake graph,

PDF

___

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