Super (a, d)-Cn-antimagic total labeling of grid graph Pn×Pm

L. Susilowati, M. Zamrud, D. P.F. Anggraeni

Research output: Contribution to journalArticlepeer-review


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, Hi 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 (Pn × Pm) with cover is H = C4, C6 for some value of d are possible and its application using computer programming.

Original languageEnglish
Pages (from-to)53-73
Number of pages21
JournalFar East Journal of Mathematical Sciences
Issue number1
Publication statusPublished - Apr 2014


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


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