The H-super(anti)magic decompositions of antiprism graphs
Hendy · AIP conference proceedings · 2016
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(G j) = Ø for i ≠ j, and ∪i=1t 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 L-decompositions 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.