IJPAM: Volume 89, No. 4 (2013)

WHEEL AS AN EDGE-MAGIC GRAPH

Yehuda Ashkenazi
Department of Computer Sciences and Mathematics
Ariel University
Ariel, ISRAEL


Abstract. An image of a plane graph, $G=(V,E)$ of order $n$ and size $m$, is said to be an edge-magic plane graph if there is a bijection $f: E \rightarrow \{1,2,..,m\}$ such that for all $s-side$ faces of $G$, except the infinite face, the sum of the labels of its edges is a constant $k(s)$. Such a bijection will be called an edge-magic plane labeling of $G$. In case that all the finite sides of a graph $G$ having the same size we will be interested in determining the minimum and the maximum number, $k$, such that there exists an edge-magic plane labeling of $G$, in which $k$ 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
Year: 2013
Volume: 89
Issue: 4