期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2019
卷号：16
期号：2
页码：125-144
DOI：10.1016/j.akcej.2018.01.014
语种：English
出版社：Elsevier
摘要：AbstractAk-magic labelingof a finite, simple graph with|V(G)|=pand|E(G)|=q,is a bijection from the set of edges into the integers{1,2,3,…,q}such that the vertex setVcan be partitioned intoksetsV1,V2,V3,…,Vk,1≤k≤p,and each vertex in the setVihas the same vertex sum and any two distinct vertices in different sets have different vertex sum, where a vertex sum is the sum of the labels of all edges incident with that vertex. A graph is calledk-magicif it hask-magic labeling, for somek,1≤k≤p.The study ofk-magic labeling is interesting, since all magic graphs are 1-magic and all antimagic graphs arep-magic. In this paper, we discuss thek-magicness of the Complete bipartite graphKp,p,where1≤k≤2p.
