On spectra of VMT labelings of complete bipartite graphs
Talk on the DiMaS seminar.
Let 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 wλ(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 n2 feasible values of the spectra of Kn,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 at
Talk given at the DiMaS seminar, V©B - TU Ostrava, 4th October 2005.
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