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Displaying similar documents to “Geodetic sets in graphs”

On Minimal Geodetic Domination in Graphs

Hearty M. Nuenay, Ferdinand P. Jamil (2015)

Discussiones Mathematicae Graph Theory

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Let G be a connected graph. For two vertices u and v in G, a u-v geodesic is any shortest path joining u and v. The closed geodetic interval IG[u, v] consists of all vertices of G lying on any u-v geodesic. For S ⊆ V (G), S is a geodetic set in G if ∪u,v∈S IG[u, v] = V (G). Vertices u and v of G are neighbors if u and v are adjacent. The closed neighborhood NG[v] of vertex v consists of v and all neighbors of v. For S ⊆ V (G), S is a dominating set in G if ∪u∈S NG[u] = V (G). A geodetic...

Further results on radial graphs

Kumarappan Kathiresan, G. Marimuthu (2010)

Discussiones Mathematicae Graph Theory

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In a graph G, the distance d(u,v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius of the graph and the maximum eccentricity is called the diameter of the graph. The radial graph R(G) based on G has the vertex set as in G, two vertices u and v are adjacent in R(G) if the distance between them in G is equal to the radius of G....

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.