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Locally regular graphs

Bohdan Zelinka (2000)

Mathematica Bohemica

A graph G is called locally s -regular if the neighbourhood of each vertex of G induces a subgraph of G which is regular of degree s . We study graphs which are locally s -regular and simultaneously regular of degree r .

Location-domatic number of a graph

Bohdan Zelinka (1998)

Mathematica Bohemica

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.

Logconcave random graphs.

Frieze, Alan, Vempala, Santosh, Vera, Juan (2010)

The Electronic Journal of Combinatorics [electronic only]

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