# IJPAM: Volume 98, No. 3 (2015)

**WHEEL AS A VERTEX-EDGE-MAGIC PLANE 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 a *vertex-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 vertices and edges is a constant . Such a bijection will be called a vertex-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 a vertex-edge-magic labeling of , in which is the sum of the vertex and edge labeling of each face. In this paper we find such a minimum and maximum numbers for a wheel with even order.

**Received: **August 21, 2014

**AMS Subject Classification: **

**Key Words and Phrases: **magic graph, plane graph, wheel, minimal magic graph, maximal magic graph, (1,1,0) magic

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**DOI: 10.12732/ijpam.v98i3.3**

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:**2015

**Volume:**98

**Issue:**3

**Pages:**313 - 321

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**This work is licensed under the Creative Commons Attribution International License (CC BY).**