期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2015
卷号：12
期号：1
页码：40-46
DOI：10.1016/j.akcej.2015.06.006
语种：English
出版社：Elsevier
摘要：Abstract Let G be a graph with vertex set V and edge set E such that | V | = p and | E | = q . We denote this graph by ( p , q ) -graph. For integers k ≥ 0 , define a one-to-one map f from E to { k , k + 1 , … , k + q − 1 } and define the vertex sum for a vertex v as the sum of the labels of the edges incident to v . If such an edge labeling induces a vertex labeling in which every vertex has a constant vertex sum ( mod p ) , then G is said to be k -edge magic ( k -EM). In this paper, we show that a maximal outerplanar graph of orders p = 4, 5, 7 are k -EM if and only if k ≡ 2 ( mod p ) and obtain all maximal outerplanar graphs that are k -EM for k = 3, 4. Finally we characterize all ( p , p − h ) -graphs that are k -EM for h ≥ 0 . We conjecture that a maximal outerplanar graph of prime order p is k -EM if and only if k ≡ 2 ( mod p ) .
