Super (a, d)-Cycle-Antimagic Total Labeling on Triangular Ladder Graph and Generalized Jahangir Graph

[摘要] Let G(V (G), E(G)) be a finite simple graph with |V (G)| =Gand |E(G)| = eG. Let H be a subgraph of G. The graph G is said to be (a, d)-H-antimagic covering if every edge in G belongs to at least one of the subgraphs G isomorphic to H and there is a bijective function ξ : V ∪ E → {1, 2, ,νG+ eG} such that all subgraphs H' isomorphic to H, the H' -weights w(H')=∑v∈V(H')ξ(v)+∑e∈E(H')ξ(e) constitutes an arithmetic progression {a, a + d, a + 2d, , a + (t - 1)d}, where a and d are positive integers and t is the number of subgraphs G isomorphic to H. Such a labeling is called super if the vertices contain the smallest possible labels. This research provides super (a, d)-C3-antimagic total labelng on triangular ladder TLnfor n ≥ 2 and super (a, d)-Cs+2-antimagic total labeling on generalized Jahangir Jk,sfor k ≥ 2 and s ≥ 2.

[发布机构] Combinatorial Research Group, Department of Mathematics, Sebelas Maret University, Surakarta, Indonesia^1

[效力级别] 教育 [学科分类] 发展心理学和教育心理学

[关键词] Antimagic;Arithmetic progressions;Bijective functions;Finite simple graphs;Graph G;Ladder graphs;Positive integers;Subgraphs