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In this paper, we show that if the second largest eigenvalue of a d-regular graph is less than d − 2(k−1) d+1 , then the graph is k-edge-connected. When k is 2 or 3, we prove stronger results. Let ρ(d) denote the largest root of x3 − (d− 3)x2 − (3d− 2)x− 2 = 0. We show that if the second largest eigenvalue of a d-regular graph G is less than ρ(d), then G is… (More)

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

Let G be an irregular graph on n vertices with maximum degree ∆ and diameter D. We show that ∆ − λ1 > 1 nD , where λ1 is the largest eigenvalue of the adjacency matrix of G. We also study the effect of adding or removing few edges on the spectral radius of a regular graph. 1 Preliminaries Our graph notation is standard (see West [22]). For a graph G, we… (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 ∈ {2, 3}. More precisely, we show that if the second largest eigenvalue of a d-regular graph G is less than d − 2k−1 d+1 , then G contains at least k edge-disjoint spanning trees, when k ∈… (More)

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

Article history: Received 14 April 2013 Available online 5 March 2014

Article history: Received 4 September 2009 Accepted 11 September 2009 Available online xxxx Submitted by R.A. Brualdi AMS classification: 05C50 05E99

- Orest Bucicovschi, Sebastian M. Cioaba
- Discrete Applied Mathematics
- 2008

In this note, we study the degree distance of a graph which is a degree analogue of the Wiener index. Given n and e, we determine the minimum degree distance of a connected graph of order n and size e.

- 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, 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 λ1 be the greatest eigenvalue and λn 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 Δ− λ1 > nΔ− 2m n(D(nΔ− 2m)+ 1) 1 n(D + 1) , where Δ is the maximum degree of G. The inequality improves previous bounds of Stevanović and of Zhang. It also implies that a… (More)

- Michael Cavers, Sebastian M. Cioaba, +5 authors Michael J. Tsatsomeros
- 2012

The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic polynomials of its adjacency and skew-adjacency matrices;… (More)