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The (directed) distance from a vertex to a vertex in a strong digraph is the length of a shortest - (directed) path in . The eccentricity of a vertex of is the distance from to a vertex furthest from in . The radius rad is the minimum eccentricity among the vertices of and the diameter diam is the maximum eccentricity. A central vertex is a vertex with eccentricity and the subdigraph induced by the central vertices is the center . For a central vertex in a strong digraph...
For a vertex in a graph , the set consists of those vertices of whose distance from is 2. If a graph contains a set of vertices such that the sets , , form a partition of , then is called a -step domination graph. We describe -step domination graphs possessing some prescribed property. In addition, all -step domination paths and cycles are determined.
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