Dalibor Froncek

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A vertex magic total (VMT) labeling of a graph G = (V,E) is a bijection from the set of vertices and edges to the set of integers defined by λ : V ∪E → {1, 2, . . . , |V | + |E|} so that for every x ∈ V , w(x) = λ(x)+ ∑ xy∈E λ(xy) = k, for some integer k. A VMT labeling is said to be a super VMT labeling if the vertices are labeled with the smallest(More)
Let G = (V,E) be a graph of order n. A distance magic labeling of G is a bijection l : V → {1, 2, . . . , n} for which there exists a positive integer k such that ∑ x∈N(v) l(x) = k for all v ∈ V , where N(v) is the open neighborhood of v. In this paper we deal with circulant graphs C(1, p). The circulant graph Cn(1, p) is the graph on the vertex set V =(More)
Proof: The proof is by induction on |V (G)| + |E(G)|. The smallest graph as described in the lemma is K1,3, for which the statement holds. This gives the start of our induction. Let x = |X| and y = |Y |. If there exists a vertex v in Y of degree at least 4, then delete any edge e incident to v. The subset A of G− e guaranteed by the inductive hypothesis is(More)
It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bipartite graph Kn,n with a perfect matching removed can be covered by k bicliques, then n ≤ ( k b k 2 c ) . We give a slightly simplified proof and we show that the result is tight. Moreover we use the result to prove analogous bounds for coverings of some other classes of graphs by(More)
Let G be a finite , simple , undirected graph . The graph G is selfcompletementary if G is isomorphic to its complement G # ; in symbols , G . G # . It is well known that a selfcomplementary graph of order n exists if f n ; 0 or 1 (mod 4) . Moreover , a regular selfcomplementary graph of order n exists if f n ; 1 (mod 4) . The objective of this paper is to(More)