- Title
- Sparse semi-magic squares and vertex-magic labelings
- Creator
- Gray, I. D.; MacDougall, James A.
- Relation
- Ars Combinatoria Vol. 80, p. 225-242
- Relation
- http://bkocay.cs.umanitoba.ca/arscombinatoria/Vol80.html
- Publisher
- Dept. of Combinatorics and Optimization, University of Waterloo
- Resource Type
- journal article
- Date
- 2006
- Description
- We introduce a generalisation of the traditional magic square which proves useful in the construction of magic labelings of graphs. An order n sparse semi-magic square is an x n array containing the entries 1,2, ..., m (for some m < n₂) once each with the remainder of its entires 0, and its rows and columns have a constant sum κ. We discover some of the basic properties of such arrays and provide constructions for squares of all orders n ≥3. We also show how these arrays can be used to produce vertex-magic labelings for certain families of graphs.
- Subject
- magic squares; graphs; vertex-magic lableings
- Identifier
- http://hdl.handle.net/1959.13/26848
- Identifier
- uon:1158
- Identifier
- ISSN:0381-7032
- Language
- eng
- Reviewed
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