A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.
A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.
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