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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/26848

Title: Sparse semi-magic squares and vertex-magic labelings
Author/Creator: Gray, I. D.; MacDougall, James A.
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.
Relation: Ars Combinatoria Vol. 80, p. 225-242
Relation: http://bkocay.cs.umanitoba.ca/arscombinatoria/Vol80.html
Date: 2006
Publisher: Dept. of Combinatorics and Optimization, University of Waterloo
Keyword(s): magic squares; graphs; vertex-magic lableings
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/26848
Identifier: ISSN:0381-7032

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