On the Existence of n-Tuple Magic Rectangles

PHAISATCHA, INPOONJAI and THIRADET, JIARASUKSAKUN (2015) On the Existence of n-Tuple Magic Rectangles. In: Third International Conference on Advances in Applied Science and Environmental Engineering - ASEE 2015, 11-12 APRIL 2015, Kuala Lumpur, Malaysia.

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Abstract

Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph G is called degree-magic if there is a labelling of the edges by integers 1, 2, ..., | E(G) | such that the sum of the labels of the edges incident with any vertex v is equal to (1 | E(G) |)deg(v) / 2. In this paper we generalize magic rectangles to be n -tuple magic rectangles, and prove the necessary and sufficient conditions for the existence of even n - tuple magic rectangles. Using this existence we identify the sufficient condition for degree-magic labellings of the n -fold selfunion of complete bipartite graphs to exist.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: magic squares, magic rectangles, degree-magic graphs
Depositing User: Mr. John Steve
Date Deposited: 07 May 2019 10:14
Last Modified: 07 May 2019 10:14
URI: http://publications.theired.org/id/eprint/2002

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