[HTML][HTML] Connectivity of Kronecker products with complete multipartite graphs
W Wang, Z Yan�- Discrete Applied Mathematics, 2013 - Elsevier
W Wang, Z Yan
Discrete Applied Mathematics, 2013•ElsevierWe study connectivity of a Kronecker product of a general graph G with a complete
multipartite graph [Formula: see text], where the parameters pk, k= 1,…, r satisfy certain
conditions. Precisely, we prove that [Formula: see text], where the sequence p1, p2,…, pr
satisfies (1) r≥ 3,(2) p1≤ p2≤⋯≤ pr,(3)∑ i= 1r− 2pi≥ pr− 1 and (4)∑ i= 1r− 1pi≥ pr.
multipartite graph [Formula: see text], where the parameters pk, k= 1,…, r satisfy certain
conditions. Precisely, we prove that [Formula: see text], where the sequence p1, p2,…, pr
satisfies (1) r≥ 3,(2) p1≤ p2≤⋯≤ pr,(3)∑ i= 1r− 2pi≥ pr− 1 and (4)∑ i= 1r− 1pi≥ pr.
We study connectivity of a Kronecker product of a general graph G with a complete multipartite graph [Formula: see text] , where the parameters pk,k=1,…,r satisfy certain conditions. Precisely, we prove that [Formula: see text] , where the sequence p1,p2,…,pr satisfies (1) r≥3, (2) p1≤p2≤⋯≤pr, (3) ∑i=1r−2pi≥pr−1 and (4) ∑i=1r−1pi≥pr.
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