期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2017
卷号：14
期号：2
页码：158-164
DOI：10.1016/j.akcej.2017.02.001
语种：English
出版社：Elsevier
摘要：Abstract A graph labeling is a mapping that assigns numbers to graph elements. The domain can be the set of all vertices, the set of all edges or the set of all vertices and edges. A labeling in which domain is the set of vertices and edges is called a total labeling. For a graph G with the vertex set V ( G ) and the edge set E ( G ) , a total labeling f : V ( G ) ∪ E ( G ) → { 1 , 2 , 3 , … , | V ( G ) | + | E ( G ) | } is called an ( a , d ) -edge antimagic total labeling if the set of edge weights { f ( x ) + f ( x y ) + f ( y ) : x y ∈ E ( G ) } forms an arithmetic progression with initial term a and common difference d . An ( a , d ) -edge antimagic total labeling is called a super ( a , d ) -edge antimagic total labeling if the smallest labels are assigned to the vertices. In this paper, we investigate the super ( a , d ) -edge-antimagic total labeling of a subclass of trees called subdivided stars for all possible values of d , mainly d = 1 , 3 .
关键词：KeywordsenSuper ( a , d ) -EAT labelingStarsSubdivided stars
