IJPAM: Volume 98, No. 3 (2015)

WHEEL AS A VERTEX-EDGE-MAGIC PLANE 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 a vertex-edge-magic plane graph if there is a bijection $f:V\cup E \rightarrow \{1,2,..,n+m\}$ such that for all $s-side$ faces of $G$, except the infinite face, the sum of the labels of its vertices and edges is a constant $k(s)$. Such a bijection will be called a vertex-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 a vertex-edge-magic labeling of $G$, in which $k$ 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 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: 2015
Volume: 98
Issue: 3
Pages: 313 - 321


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