A Special Case of a Game based on Vertex-Magic Total Labelings

E. Boudreau, B. Hartnell, K. Schmeisser and J. Whiteley
Saint Mary’s University, Halifax, Nova Scotia, Canada


Abstract:  For a given graph G, let V be the number of vertices and E be the 
number of edges. Consider a labeling of the vertices and edges which is a 
one-to-one mapping of the set of integers {1,2,…,V + E} onto the vertices 
and edges of the graph, with the property that for every vertex the sum of 
the labels assigned to that vertex and all edges incident with it is some 
constant k. Although work to date has been on deciding which graphs admit 
such a labeling (called a vertex-magic total labeling), we shall consider a 
game based on this concept. This report describes a winning strategy for a 
special family of graphs and is meant to supplement a separate paper [1].