Regular sparse anti-magic squares with maximum density

被引：0

作者：

Chen, Kejun ^{[1
]}

Li, Wen ^{[1
]}

Chen, Guangzhou ^{[2
]}

Wei, Ruizhong ^{[3
]}

机构：

[1] Yancheng Teachers Univ, Dept Math, Yancheng 224051, Peoples R China

[2] Hebei Normal Univ, Math & Informat Sci Coll, Shijiazhuang 050024, Peoples R China

[3] Lakehead Univ, Dept Comp Sci, Thunder Bay, ON P7B 5E1, Canada

来源：

ARS COMBINATORIA | 2016年 / 127卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Magic square; Anti-magic square; Sparse; Regular; Vertex-magic labeling;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Sparse anti-magic squares are useful in constructing vertex-magic labelings for bipartite graphs. An n x n array based on {0,1,..., nd} is called a sparse anti-magic square of order n with density d (d < n), denoted by SAMS(n, d), if its row-sums, column-sums and two main diagonal sums constitute a set of 2n + 2 consecutive integers. A SAMS(n, d) is called regular if there are d positive entries in each row, each column and each main diagonal. In this paper, some constructions of regular sparse anti-magic squares are provided and it is shown that there exists a regular SAMS(n, n-1) if and only if n >= 4.

引用

页码：167 / 183

页数：17