Super (a*, d*)-ℋ-antimagic total covering of second order of shackle graphs

Agustin, Ika Hesti; Dafik, Dafik; Nisviasari, Rosanita; Prihandini, R. M.

doi:10.1088/1742-6596/943/1/012060

J. Phys.: Conf. Ser.

2017

DOI: 10.1088/1742-6596/943/1/012060

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Super (a, d)-ℋ-antimagic total covering of second order of shackle graphs

Ika Hesti Agustin

Dafik Dafik

Rosanita Nisviasari

et al.

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2019

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“…Furthermore, Dafik et al [6,7] studied about -super antimagicness of disconnected graphs as well as constructions of -antimagic graphs using smaller edge antimagic graphs. More results about super ( , )-antimagic total labeling can be seen in [8][9][10][11].…”

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confidence: 94%

On H-Supermagic Labelings of m-Shadow of Paths and Cycles

Agustin

Susanto

Dafik

et al. 2019

International Journal of Mathematics and Mathematical Sciences

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A simple graph G=(V,E) is said to be an H-covering if every edge of G belongs to at least one subgraph isomorphic to H. A bijection f:V∪E→{1,2,3,…,V+E} is an (a,d)-H-antimagic total labeling of G if, for all subgraphs H′ isomorphic to H, the sum of labels of all vertices and edges in H′ form an arithmetic sequence {a,a+d,…,(k-1)d} where a>0, d≥0 are two fixed integers and k is the number of all subgraphs of G isomorphic to H. The labeling f is called super if the smallest possible labels appear on the vertices. A graph that admits (super) (a,d)-H-antimagic total labeling is called (super) (a,d)-H-antimagic. For a special d=0, the (super) (a,0)-H-antimagic total labeling is called H-(super)magic labeling. A graph that admits such a labeling is called H-(super)magic. The m-shadow of graph G, Dm(G), is a graph obtained by taking m copies of G, namely, G1,G2,…,Gm, and then joining every vertex u in Gi, i∈{1,2,…,m-1}, to the neighbors of the corresponding vertex v in Gi+1. In this paper we studied the H-supermagic labelings of Dm(G) where G are paths and cycles.

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confidence: 94%

On H-Supermagic Labelings of m-Shadow of Paths and Cycles

Agustin

Susanto

Dafik

et al. 2019

International Journal of Mathematics and Mathematical Sciences

Self Cite

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Super (a, d)-ℋ-antimagic total covering of second order of shackle graphs

Cited by 1 publication

References 4 publications

On H-Supermagic Labelings of m-Shadow of Paths and Cycles

On H-Supermagic Labelings of m-Shadow of Paths and Cycles

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