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

International Conference on Mathematics: Education, Theory and Application

数学;教育

Roswitha, Mania^1 ; Amanda, Anna^1 ; Martini, Titin Sri^1 ; Winarno, Bowo^1

Combinatorial Research Group, Department of Mathematics, Sebelas Maret University, Surakarta, Indonesia^1

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

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/855/1/012037/pdf
DOI  :  10.1088/1742-6596/855/1/012037

学科分类：发展心理学和教育心理学

来源: IOP

【 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.