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Displaying similar documents to “The directed distance dimension of oriented graphs”

Exact 2 -step domination in graphs

Gary Chartrand, Frank Harary, Moazzem Hossain, Kelly Schultz (1995)

Mathematica Bohemica

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For a vertex v in a graph G , the set N 2 ( v ) consists of those vertices of G whose distance from v is 2. If a graph G contains a set S of vertices such that the sets N 2 ( v ) , v ∈ S , form a partition of V ( G ) , then G is called a 2 -step domination graph. We describe 2 -step domination graphs possessing some prescribed property. In addition, all 2 -step domination paths and cycles are determined.

Digraphs contractible onto * K 3

Stefan Janaqi, François Lescure, M. Maamoun, Henry Meyniel (1998)

Mathematica Bohemica

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We show that any digraph on n ≥ 3 vertices and with not less than 3 n - 3 arcs is contractible onto * K 3 .

Location-domatic number of a graph

Bohdan Zelinka (1998)

Mathematica Bohemica

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A subset D of the vertex set V ( G ) of a graph G is called locating-dominating, if for each x ∈ V ( G ) - D there exists a vertex y → D adjacent to x and for any two distinct vertices x 1 , x 2 of V ( G ) - D the intersections of D with the neighbourhoods of x 1 and x 2 are distinct. The maximum number of classes of a partition of V ( G ) whose classes are locating-dominating sets in G is called the location-domatic number of G . Its basic properties are studied.

On 2 -extendability of generalized Petersen graphs

Nirmala B. Limaye, Mulupuri Shanthi C. Rao (1996)

Mathematica Bohemica

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Let G P ( n , k ) be a generalized Petersen graph with ( n , k ) = 1 , n > k ≥ 4 . Then every pair of parallel edges of G P ( n , k ) is contained in a 1-factor of G P ( n , k ) . This partially answers a question posed by Larry Cammack and Gerald Schrag [Problem 101, Discrete Math. 73(3), 1989, 311-312].