## Abstract

A graph G = (V(G), E(G)) admits an (H1, H2, ..., Hk) -covering if every edge in G belongs to at least one of the subgraphs Hi, 1 ≤ i ≤ k. If for every i, H_{i} isomorphic to a given graph H, then G is called having an H-covering. An (a, d) -H-antimagic total labeling of graph G is a bijection f:V(G)∪ E(G)→{1, 2, ..., |V(G)|+|E(G)|} such that the set of weight of every subgraph H′ which is isomorphic to H is a + (a + d) +...+ (a + (t - 1)d), where a and d are positive integers, and t is the number of subgraph of G isomorphic to H. If f: V(G) → {1, 2, ..., |V(G)|}, then G is called having a super (a, d)-H-antimagic total labeling. This project applying this labeling to the grid graph (P_{n} × P_{m}) with cover is H = C_{4}, C_{6} for some value of d are possible and its application using computer programming.

Original language | English |
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Pages (from-to) | 53-73 |

Number of pages | 21 |

Journal | Far East Journal of Mathematical Sciences |

Volume | 87 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 2014 |

## Keywords

- (A,d)-H-antimagic total labeling
- Covering
- Super (a,d)-H-antimagic total labeling
- Total labeling

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