The Restricted Edge-Connectivity of Kautz Undirected Graphs

نویسندگان

Ying-Mei Fan

Jun-Ming Xu

Min Lu

چکیده

A connected graph is said to be super edge-connected if every minimum edge-cut isolates a vertex. The restricted edge-connectivity λ′ of a connected graph is the minimum number of edges whose deletion results in a disconnected graph such that each connected component has at least two vertices. A graph G is called λ′-optimal if λ′(G) = min{dG(u)+dG(v)−2 : uv is an edge in G}. This paper proves that for any d and n with d ≥ 2 and n ≥ 1 the Kautz undirected graph UK(d, n) is λ′-optimal except UK(2, 1) and UK(2, 2) and, hence, is super edge-connected except UK(2, 2).

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