Brešar, Boštjan; Špacapan, Simon On the connectivity of the direct product of graphs. (English) Zbl 1170.05041 Australas. J. Comb. 41, 45-56 (2008). Summary: In this note we show that the edge-connectivity \(\lambda(G\times H)\) of the direct product of graphs \(G\) and \(H\) is bounded below by \(\min\{\lambda(G)|E(H)|, \lambda(H)|E(G)|, \delta(G\times H)\}\) and above by \(\min\{2\lambda(G)|E(H)|, 2\lambda(H)|E(G)|, \delta(G\times H)\}\) except in some special cases when \(G\) is a relatively small bipartite graph, or both graphs are bipartite. Several upper bounds on the vertex-connectivity of the direct product of graphs are also obtained. Cited in 15 Documents MSC: 05C40 Connectivity PDFBibTeX XMLCite \textit{B. Brešar} and \textit{S. Špacapan}, Australas. J. Comb. 41, 45--56 (2008; Zbl 1170.05041)