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)

Terwilliger [15] has given the diameter bound d < (s 1)(k 1) + 1 for distance-regular graphs with girth 2s and valency k. We show that the only distance-regular graphs with even girth which reachâ€¦ (More)

There are only finitely many distance-regular graphs of fixed valency greater than two Abstract In this paper we prove the Bannai-Ito conjecture, namely that there are only finitely manyâ€¦ (More)

Let G be a graph of order n such that âˆ‘n i=0(âˆ’1)iaiÎ»nâˆ’i and âˆ‘n i=0(âˆ’1)ibiÎ»nâˆ’i are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, respectively. We show thatâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2011

We show that there is a disparity in fractal scaling behavior of the core and peripheral parts of empirical small-world scale-free networks. We decompose the network into a core and a periphery andâ€¦ (More)

In this note, we consider connected graphs with exactly two main eigenvalues. We will give several constructions for them, and as a consequence we show a family of those graphs with an unboundedâ€¦ (More)

Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphsâ€¦ (More)

Given a metric d on a finite set X, a realization of d is a triple (G,Ï†,w) consisting of a graph G = (V,E), a labeling Ï† : X â†’ V , and a weighting w : E â†’ R>0 such that for all x, y âˆˆ X the length ofâ€¦ (More)