IJPAM: Volume 89, No. 4 (2013)
Department of Computer Sciences and Mathematics
Abstract. An image of a plane graph, of order and size , is said to be an edge-magic plane graph if there is a bijection such that for all faces of , except the infinite face, the sum of the labels of its edges is a constant . Such a bijection will be called an edge-magic plane labeling of . In case that all the finite sides of a graph having the same size we will be interested in determining the minimum and the maximum number, , such that there exists an edge-magic plane labeling of , in which is the sum of the edge labeling of each face. In this paper we find such a minimum and maximum numbers for a wheel with even order. Furthermore we conjecture that the same formula is valid for the odd case.
Received: September 23, 2013
AMS Subject Classification:
Key Words and Phrases: magic graph, plane graph, wheel, edge magic, minimal magic graph, maximal magic graph
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DOI: 10.12732/ijpam.v89i4.12 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395