Displaying similar documents to “Geodetic graphs which are homeomorphic to complete graphs”

Diameter-invariant graphs

Ondrej Vacek (2005)

Mathematica Bohemica

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The diameter of a graph G is the maximal distance between two vertices of  G . A graph G is said to be diameter-edge-invariant, if d ( G - e ) = d ( G ) for all its edges, diameter-vertex-invariant, if d ( G - v ) = d ( G ) for all its vertices and diameter-adding-invariant if d ( G + e ) = d ( e ) for all edges of the complement of the edge set of G . This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.

Geodetic sets in graphs

Gary Chartrand, Frank Harary, Ping Zhang (2000)

Discussiones Mathematicae Graph Theory

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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...

Chordal Graphs

Broderick Arneson, Piotr Rudnicki (2006)

Formalized Mathematics

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We are formalizing [9, pp. 81-84] where chordal graphs are defined and their basic characterization is given. This formalization is a part of the M.Sc. work of the first author under supervision of the second author.