Abstract
An edge cutset E⊂E(G) of a graph G is called a restricted edge cutset if every component of G−E has order at least 2. We let λ′(G) denote the minimum cardinality of a restricted edge cutset of G, and let δ′(G) denote the minimum of degG(x)+degG(y)−2 as x and y range over all adjacent vertices of G. We let λ(G) and δ(G) denote the edge connectivity and the minimum degree of G, respectively. Among other results, we show that if G1 and G2 are graphs such that λ(Gi)=δ(Gi)≥2 and λ′(Gi)=δ′(Gi)≥2 for each i=1,2, then λ′(G1⊗G2)=δ′(G1⊗G2)=min{δ′(G1)+2δ(G2),δ′(G2)+2δ(G1)}, where G1⊗G2 denotes the cartesian product of G1 and G2.
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