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Maximal Energy Graphs
We show that if G is a graph on n vertices, then E(G)@?n21+n must hold, and we give an infinite family of graphs for which this bound is sharp. Expand
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments inExpand
A New Family of Distance-Regular Graphs with Unbounded Diameter
We construct distance-regular graphs with the same-classical-parameters as the Grassman graphs on the e-dimensional subspaces of a (2e+1)-dimensional space over an arbitrary finite field. ThisExpand
Open problems in the spectral theory of signed graphs
Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature) assigning a positive or negative sign to each edge. Expand
On the Hyperbolicity of Chordal Graphs
Abstract. The hyperbolicity $ \delta^* \ge 0 $ of a metric space in Gromov's sense can be viewed as a measure of how "tree-like" the space is, since those spaces for which $ \delta^* = 0 $ holdsExpand
On the connectedness of the complement of a ball in distance-regular graphs
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 beExpand
On graphs with smallest eigenvalue at least -3 and their lattices.
In this paper, we show that a connected graph with smallest eigenvalue at least -3 and large enough minimal degree is 2-integrable. This result generalizes a 1977 result of Hoffman for connectedExpand
An improvement of the Ivanov bound
AbstractLet Γ be a distance-regular graph of diameterd, valencyk andr=max{i|(ci,bi)=(c1,b1)}. In this paper, we prove that $$d< \frac{1}{2}k^3 r.$$
On the multiplicity of eigenvalues of distance-regular graphs
Abstract We rule out the infinite series of feasible intersection array {μ(2μ + 1), (μ − 1)(2μ + 1), μ2, μ; 1, μ, μ(μ − 1), μ(2μ + 1), μ ⩾ 2}.
Tight Distance-Regular Graphs
AbstractWe consider a distance-regular graph Γ with diameter d ≥ 3 and eigenvalues k = θ0 > θ1 > ... > θd. We show the intersection numbers a1, b1 satisfy $$\left( {\theta _1 + \frac{k}{{a_1 + 1}}}Expand