# IJPAM: Volume 89, No. 4 (2013)

**WHEEL AS AN EDGE-MAGIC GRAPH**

Department of Computer Sciences and Mathematics

Ariel University

Ariel, ISRAEL

**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**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2013

**Volume:**89

**Issue:**4