Conditional Graph Theory III: Independence Numbers
The theory of tournaments: A miniature mathematical system
On the Problem of Reconstructing a Tournament from Subtournaments.
Every forest can be obtained from a minimal block.
On the Corona of Two Graphs. (Short Communication).
On the Corona of Two Graphs.
The degree sets of connected infinite graphs
Planar Permutation Graphs
On the number of cycles in a graph
Minimum maximal graphs with forbidden subgraphs
Which directed graphs have a solution?
On the Point-Core of a Graph.
The Regulation Number of a Graph
Boolean Operations on Graphs.
The number of archiral trees.
On the planarity of 2-complexes
Line minimal Boolean forests
Geodetic sets in graphs
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
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 , 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”
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