2010/02/12 by Rija Erveš, Rija Erves, Erves, Rija +3 · 1 citation
Computer Science · Engineering · Materials Science · Mathematics · #05C40 #Combinatorics (math.CO) #FOS: Mathematics #Graphene and Nanomaterials Applications #Graphene research and applications #Interconnection Networks and Systems #math.CO #msc:05C40
paper · pdf · doi:10.48550/arxiv.1002.2508
arxiv created 2010/02/12 · openalex publication_date 2010/02/12 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mixed connectivity is a generalization of vertex and edge connectivity. A graph is (p,0)-connected, p>0, if the graph remains connected after removal of any p-1 vertices. A graph is (p,q)-connected, p≥ 0, q>0, if it remains connected after removal of any p vertices and any q-1 edges. Cartesian graph bundles are graphs that generalize both covering graphs and Cartesian graph products. It is shown that if graph F is (pF,qF)-connected and graph B is (pB,qB)-connected, then Cartesian graph bundle G with fibre F over the base graph B is (pF+pB,qF+qB)-connected. Furthermore, if qF,qB>0, then G is also (pF+pB+1,qF+qB-1)-connected. Finally, let graphs Gi, i=1,...,n, be (pi,qi)-connected and let k be the number of graphs with qi>0. The Cartesian graph product G=G1\Box G2\Box ... \Box Gn is (∑ pi,∑ qi)-connected, and, for k≥ 1, it is also (∑ pi+k-1,∑ qi-k+1)-connected.