Edge-Magic Total Labelings
W. D. Wallis · Birkhäuser Boston eBooks · 2001
An edge-magic total labeling on a graph G is a one-to-one map λ from V ( G ) ∪ E ( G ) onto the integers 1, 2, …, v + e , where v = V ( G )\ and e = E ( G ), with the property that, given any edge ( xy ), k ( x ) + k ( xy ) + k ( y ) = k for some constant k . In other words, wt ( xy ) = K for any choice of edge xy . k is called the magic sum of G . Any graph with an edge-magic total labeling will be called edge-magic .