The Connected and Disjoint Union of Semi Jahangir Graphs Admit a Cycle-Super (a, d)-Atimagic Total Labeling

2015 International Conference on Mathematics, its Applications, and Mathematics Education

数学;教育

Dafik^1,2 ; Agustin, I.H.^1,3 ; Hardiyantik, D.^3

CGANT - University of Jember, Indonesia^1

Mathematics Education Department, University of Jember, Indonesia^2

Mathematics Department, University of Jember, Indonesia^3

关键词: Antimagic;    Bijective functions;    Graph G;    Positive integers;    Subgraphs;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/693/1/012006/pdf
DOI  :  10.1088/1742-6596/693/1/012006

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

We assume that all graphs in this paper are finite, undirected and no loop and multiple edges. Given a graph G of order p and size q. Let H',H be subgraphs of G. By H'-covering, we mean every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. A graph G is said to be an (a,d)-H-antimagic total labeling if there exist a bijective function f : V(G) ∪E(G) → {1, 2,,p + q} such that for all subgraphs H' isomorphicto H,the total H-weights ω(H) = form an arithmetic sequence {a, a+d, a+2d,, a+(s-1)d}, where a and d are positive integers and s is the number of all subgraphs H' isomorphic to H. Such a labeling is called super if f : V(G) → {1, 2,. ., | V(G)|}. In this paper, we will discuss a cycle-super (a,d)-atimagicness of a connected and disjoint union of semi jahangir graphs. The results show that those graphs admit a cycle-super (a,d)-atimagic total labeling for some feasible d ∈ {0,1, 2, 4, 6, 7,10,13,14}.