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Conditional Graph Theory III: Independence Numbers

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The theory of tournaments: A miniature mathematical system

Colloquium Mathematicae

On the Problem of Reconstructing a Tournament from Subtournaments.

Monatshefte für Mathematik

Every forest can be obtained from a minimal block.

Journal für die reine und angewandte Mathematik

The Regulation Number of a Graph

Publications de l'Institut Mathématique

Geodetic sets in graphs

Discussiones Mathematicae Graph Theory

For two vertices u and v of a graph G, the closed interval I[u,v] consists of u, v, and all vertices lying in some u-v geodesic in G. If S is a set of vertices of G, then I[S] is the union of all sets I[u,v] for u, v ∈ S. If I[S] = V(G), then S is a geodetic set for G. The geodetic number g(G) is the minimum cardinality of a geodetic set. A set S of vertices in a graph G is uniform if the distance between every two distinct vertices of S is the same fixed number. A geodetic set is essential if for...

Destroying symmetry by orienting edges: complete graphs and complete bigraphs

Discussiones Mathematicae Graph Theory

Our purpose is to introduce the concept of determining the smallest number of edges of a graph which can be oriented so that the resulting mixed graph has the trivial automorphism group. We find that this number for complete graphs is related to the number of identity oriented trees. For complete bipartite graphs ${K}_{s,t}$, s ≤ t, this number does not always exist. We determine for s ≤ 4 the values of t for which this number does exist.

Correction: “The smallest graph whose group is cyclic”

Czechoslovak Mathematical Journal

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