| Abstrakt: |
Let H and G be two simple graphs. The concept of an H-magic decomposition of G arises from the combination between graph decompositions and graph labeling. A family B = {G1,G2, ...,Gt} of subgraphs of G is an H-decomposition of G, if all subgraphs are isomorphic to graph H, E(Gi)∩E(Gj) = ø for i ≠ j, and Uti=1 E(Gi) = E(G). The graph G is said to be H-magic, if there exists a bijection f :V(G)∪E(G) → {1,2, ..., |V(G)∪E(G)|} such that the sum of labels of all edges and vertices of each copy of H in a decomposition is constant. The graph G is said to be (a,d)H-anti magic, if there exists a bijection f : V(G)∪E(G) → {1,2, ..., |V(G)∪E(G)|} such that the sum of labels of all edges and vertices of each copy of H in a decomposition is element of {a,a+d,a+2d, ...,a+(k-1)d}. In this paper we show that the Antiprism graph, An, for n ≥ 3 are H-decomposable, where H isomorf with sun graph, S(Cn), 3-cycle with a pendant, L, and path with length two, P2. Also we show that for n ≥ 3, the Antiprism graph An, has super magic S(Cn)-decompositions, super edge magic Ldecompositions and super edge magic P2-decompositions. In addition we show that for n ≥ 3, the Antiprism graph An, has super antimagic (8n² +2n,4n²)- S(Cn)- decompositions. [ABSTRACT FROM AUTHOR] |
