Sekundarni povzetek: |
The direct product of graphs ▫$G = (V(G),E(G))$▫ and ▫$H = (V(H),E(H))$▫ is the graph, denoted as ▫$G \times H$▫, with vertex set ▫$V(G \times H) = V(G) \times V(H)$▫, where vertices ▫$(x_1,y_1)$▫ and ▫$(x_2,y_2)$▫ are adjacent in ▫$G \times H$▫ if ▫$x_1x_2 \in E(G)$▫ and ▫$y_1y_2 \in E(H)$▫. The edge connectivity of a graph ▫$G$▫, denoted as ▫$\lambda(G)$▫, is the size of a minimum edge-cut in ▫$G$▫. We introduce a function ▫$\psi$▫ and prove the following formula ▫$$\lambda (G \times H) = \min \{2\lambda(G)|E(H)|, 2\lambda(H)|E(G)|, \delta(G \times H), \psi(G,H), \psi(H,G)\} .$$▫ We also describe the structure of every minimum edge-cut in ▫$G \times H$▫. |