WHEEL AS A VERTEX-EDGE-MAGIC PLANE GRAPH
Yehuda Ashkenazi · International Journal of Pure and Apllied Mathematics · 2015
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 ∪ E → {1, 2, .., n + m} such that for all sside 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-edgemagic 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.