On H-Supermagic Labelings of m-Shadow of Paths and Cycles

Autor: Ika Hesti Agustin, F. Susanto, Dafik, R. M. Prihandini, R. Alfarisi, I. W. Sudarsana
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2019 (2019)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
DOI: 10.1155/2019/8780329
Popis: A simple graph G=(V,E) is said to be an H-covering if every edge of G belongs to at least one subgraph isomorphic to H. A bijection f:V∪E→{1,2,3,…,V+E} is an (a,d)-H-antimagic total labeling of G if, for all subgraphs H′ isomorphic to H, the sum of labels of all vertices and edges in H′ form an arithmetic sequence {a,a+d,…,(k-1)d} where a>0, d≥0 are two fixed integers and k is the number of all subgraphs of G isomorphic to H. The labeling f is called super if the smallest possible labels appear on the vertices. A graph that admits (super) (a,d)-H-antimagic total labeling is called (super) (a,d)-H-antimagic. For a special d=0, the (super) (a,0)-H-antimagic total labeling is called H-(super)magic labeling. A graph that admits such a labeling is called H-(super)magic. The m-shadow of graph G, Dm(G), is a graph obtained by taking m copies of G, namely, G1,G2,…,Gm, and then joining every vertex u in Gi, i∈{1,2,…,m-1}, to the neighbors of the corresponding vertex v in Gi+1. In this paper we studied the H-supermagic labelings of Dm(G) where G are paths and cycles.
Databáze: Directory of Open Access Journals
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