A matching in a hypergraph H is a set of pairwise disjoint hyperedges. The matching number α (H) of H is the size of a maximum matching in H. A subset D of vertices of H is a dominating set of H if for every v ∈ V \ D there exists u ∈ D such that u and v lie in an hyperedge of H. The cardinality of a minimum dominating set of H is called the domination number of H, denoted by γ(H). It is known that for a intersecting hypergraph H with rank r, γ(H) ≤ r − 1. In this paper we present structural properties on intersecting hypergraphs with rank r satisfying the equality γ(H) = r − 1. By applying the properties we show that all linear intersecting hypergraphs H with rank 4 satisfying γ(H) = r − 1 can be constructed by the well-known Fano plane.

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Let G = (V, A) be a digraph and k ≥ 1 an integer. For u, v ∈ V , we say that the vertexand generalized Kautz digraphs G K (n, d) are good candidates for interconnection networks.

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