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In this paper, we show that if the second largest eigenvalue of a d-regular graph is less than d âˆ’ 2(kâˆ’1) d+1 , then the graph is k-edge-connected. When k is 2 or 3, we prove stronger results. Letâ€¦ (More)

- Sebastian M. Cioaba, Wiseley Wong
- ArXiv
- 2012

Partially answering a question of Paul Seymour, we obtain a sufficient eigenvalue condition for the existence of k edge-disjoint spanning trees in a regular graph, when k âˆˆ {2, 3}. More precisely, weâ€¦ (More)

An important property of strongly regular graphs is that the second subconstituent of any primitive strongly regular graph is always connected. Brouwer asked to what extent this statement can beâ€¦ (More)

- Sebastian M. Cioaba
- Discrete Mathematics
- 2006

For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k.

- Sebastian M. Cioaba
- Electr. J. Comb.
- 2007

Let G be an irregular graph on n vertices with maximum degree âˆ† and diameter D. We show that âˆ† âˆ’ Î»1 > 1 nD where Î»1 is the largest eigenvalue of the adjacency matrix of G. We also study the effect ofâ€¦ (More)

- Sebastian M. Cioaba, David A. Gregory, Willem H. Haemers
- J. Comb. Theory, Ser. B
- 2009

Article history: Received 6 December 2006 Available online 26 July 2008

- Sebastian M. Cioaba, David A. Gregory, Vladimir Nikiforov
- J. Comb. Theory, Ser. B
- 2007

Let Î»1 be the greatest eigenvalue and Î»n the least eigenvalue of the adjacency matrix of a connected graph G with n vertices, m edges and diameter D. We prove that if G is nonregular, then âˆ† âˆ’ Î»1 >â€¦ (More)

- Sebastian M. Cioaba, Felix Lazebnik, Weiqiang Li
- J. Comb. Theory, Ser. B
- 2014

Let q = pe, where p is a prime and e â‰¥ 1 is an integer. For m â‰¥ 1, let P and L be two copies of the (m + 1)-dimensional vector spaces over the finite field Fq. Consider the bipartite graph Wm(q) withâ€¦ (More)

Let G be a connected graph. This paper studies the extreme entries of the principal eigenvector x of G, the unique positive unit eigenvector corresponding to the greatest eigenvalue Î»1 of theâ€¦ (More)

- Sebastian M. Cioaba, AndrÃ© KÃ¼ndgen, Jacques VerstraÃ«te
- J. Comb. Theory, Ser. A
- 2009

We study the minimum number of complete r-partite r-uniform hypergraphs needed to partition the edges of the complete r-uniform hypergraph on n vertices and we improve previous results of Alon.