Connectivity of Cartesian product graphs

@article{Xu2006ConnectivityOC,
  title={Connectivity of Cartesian product graphs},
  author={Jun-Ming Xu and Chao Yang},
  journal={Discrete Mathematics},
  year={2006},
  volume={306},
  pages={159-165}
}
Use vi , i , i , i to denote order, connectivity, edge-connectivity and minimum degree of a graph Gi for i=1, 2, respectively. For the connectivity and the edge-connectivity of the Cartesian product graph, up to now, the best results are (G1 ×G2) 1 + 2 and (G1 ×G2) 1 + 2. This paper improves these results by proving that (G1 ×G2) min{ 1 + 2, 2 + 1} and (G1 ×G2)= min{ 1 + 2, 1v2, 2v1} if G1 and G2 are connected undirected graphs; (G1 ×G2) min{ 1 + 2, 2 + 1, 2 1 + 2, 2 2 + 1} if G1 and G2 are… CONTINUE READING

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