Sciweavers

DM
2007

Lower connectivities of regular graphs with small diameter

13 years 3 months ago
Lower connectivities of regular graphs with small diameter
Krishnamoorthy, Thulasiraman and Swamy [Minimum order graphs with specified diameter, connectivity and regularity, Networks 19 (1989) 25–46] showed that a δ-regular graph with diameter D at most 3 has (vertex-)connectivity κ at least 2, and if D ≤ 2 then the connectivity is at least κ ≥ min{δ, 3}. Likewise, Soneoka, Nakada, Imase and Peyrat [Sufficient conditions for maximally connected graphs, Discrete Mathematics 63 (1) (1987) 53–66] proved that a graph with diameter D ≤ 2 (g − 1)/2 − 1 has maximum connectivity κ = δ. In this work we generalize and improve these results for δ-regular graphs. More precisely we prove that if D ≤ 2 (g − 1)/2 + 1 then κ ≥ 2, and if D ≤ g − 1 then κ ≥ min{δ, 3}. Furthermore, we prove for g even that if D ≤ g − 2 then κ ≥ min{δ, 6}, and for bipartite δ-regular graphs we obtain that if D ≤ g−1 then κ ≥ min{δ, 4}, and if D ≤ g then κ ≥ 2. We establish similar bounds for the edge connectivity and pre...
Camino Balbuena, Xavier Marcote
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where DM
Authors Camino Balbuena, Xavier Marcote
Comments (0)