## On restricted connectivity of some Cartesian product graphs.(English)Zbl 1259.05101

Summary: A subset $$S \subset V(G)$$ is called a restricted cut, if it does not contain a neighbor-set of any vertex as its subset and $$G - S$$ is disconnected. If there exists a restricted cut $$S$$ in $$G$$, the restricted connectivity $$\kappa^1(G) = \min\{|S| :S$$ is a restricted cut of $$G\}$$. The Cartesian product graphs are considered and $$\kappa^1(G) = 2\sum^2_{i=1} k_i - 2$$ is obtained if for each $$i =1,2,\dots,n$$ ($$n \geq 3$$), $$G_i$$ is a $$k_i$$-regular $$k_i$$ connected graph of girth at least 5 and satisfies some given conditions, where $$G = G_1 \times G_2 \times \dots \times G_n$$.

### MSC:

 05C40 Connectivity 05C76 Graph operations (line graphs, products, etc.) 05C65 Hypergraphs