
On spectra of VMT labelings of complete bipartite graphsTalk on the DiMaS seminar. AbstractLet λ be an injective mapping from the set of both vertices and edges (V ∪ E) of a graph to the set of the first V+E natural numbers. The weight w_{λ}(v) of a vertex v in V is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling if the weight of each vertex is equal to the same constant h called the magic constant. The spectra of a given graph G is the set of all magic constants which can be realized by a VMT labelings of G. It was conjectured by W. Wallis et al. that all n^{2} feasible values of the spectra of K_{n,n} can be realized by some VMT labeling. So far only two different magic constants were known. We present constructions for a large set of magic constants. Talk given atTalk given at the DiMaS seminar, V©B  TU Ostrava, 4th October 2005.
