Sparse anti-magic squares and vertex-magic labelings of bipartite graphs

A sparse anti-magic square is an n × n array whose non-zero entries are the consecutive integers 1 , … , m for some m ⩽ n 2 and whose row-sums and column-sums form a set of consecutive integers. We derive some basic properties of these arrays and provide constructions for several infinite families o...

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Bibliographic Details
Published in:Discrete mathematics 2006-11, Vol.306 (22), p.2878-2892
Main Authors: Gray, I.D., MacDougall, J.A.
Format: Article
Language:English
Subjects:
Algebra
Anti-magic square
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
Graph theory
Linear and multilinear algebra, matrix theory
Magic labeling
Mathematics
Sciences and techniques of general use
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Summary:A sparse anti-magic square is an n × n array whose non-zero entries are the consecutive integers 1 , … , m for some m ⩽ n 2 and whose row-sums and column-sums form a set of consecutive integers. We derive some basic properties of these arrays and provide constructions for several infinite families of them. Our main interest in these arrays is their application to constructing vertex-magic labelings for bipartite graphs.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2006.04.032