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Tight distanceregular graphs
 J. Algebraic Combin
"... A Shilla distanceregular graph Γ (say with valency k) is a distanceregular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divides k for a Shilla distanceregular graph Γ, and for Γ we. In this paper we will show that there are finitely many Shilla ..."
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Cited by 20 (13 self)
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A Shilla distanceregular graph Γ (say with valency k) is a distanceregular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divides k for a Shilla distanceregular graph Γ, and for Γ we. In this paper we will show that there are finitely many Shilla
Distanceregular graphs
, 2014
"... This is a survey of distanceregular graphs. We present an introduction to distanceregular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distanceregular graphs since the monograph ‘BCN ’ [Brouwer, A.E., Cohen, ..."
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Cited by 14 (9 self)
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This is a survey of distanceregular graphs. We present an introduction to distanceregular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distanceregular graphs since the monograph ‘BCN ’ [Brouwer, A.E., Cohen,
Tight DistanceRegular Graphs
"... We consider a distanceregular graph \Gamma with diameter d 3 and eigenvalues k = ..."
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Cited by 12 (5 self)
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We consider a distanceregular graph \Gamma with diameter d 3 and eigenvalues k =
Eigenpolytopes Of Distance Regular Graphs
, 1998
"... Let X be a graph with vertex set V and let A be its adjacency matrix. If E is the matrix representing orthogonal projection onto an eigenspace of A with dimension m, then E is positive semidefinite. Hence it is the Gram matrix of a set of jV j vectors in R m . We call the convex hull of a such a ..."
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set of vectors an eigenpolytope of X. The connection between the properties of this polytope and the graph is strongest when X is distance regular and, in this case, it is most natural to consider the eigenpolytope associated to the second largest eigenvalue of A. The main result of this paper
Two distanceregular graphs
, 2011
"... We construct two families of distanceregular graphs, namely the subgraph of the dual polar graph of type B3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite d ..."
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We construct two families of distanceregular graphs, namely the subgraph of the dual polar graph of type B3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite
ON 3CHROMATIC DISTANCEREGULAR GRAPHS
, 2006
"... We give some necessary conditions for a graph to be 3chromatic in terms of the spectrum of the adjacency matrix. For all known distanceregular graphs it is determined whether they are 3chromatic. A start is made with the classification of 3chromatic distanceregular graphs, and it is shown that ..."
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We give some necessary conditions for a graph to be 3chromatic in terms of the spectrum of the adjacency matrix. For all known distanceregular graphs it is determined whether they are 3chromatic. A start is made with the classification of 3chromatic distanceregular graphs, and it is shown
On electric resistances for distanceregular graphs
 European Journal of Combinatorics
"... We investigate the behavior of electric potentials on distanceregular graphs, and extend some results of a prior paper, [12]. Our main result, Theorem 4 below, shows(together with Corollary 3) that if distance is measured by the electric resistance between points then all points are close to being ..."
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Cited by 2 (2 self)
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We investigate the behavior of electric potentials on distanceregular graphs, and extend some results of a prior paper, [12]. Our main result, Theorem 4 below, shows(together with Corollary 3) that if distance is measured by the electric resistance between points then all points are close to being
A Questionable DistanceRegular Graph
"... Abstract In this paper, we introduce distanceregular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distanceregular graphs and sh ..."
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Abstract In this paper, we introduce distanceregular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distanceregular graphs
Distanceregular graphs
, 1986
"... Menger's Theorem states that in a 3connected graph, any two vertices are joined by three openly disjoint paths. Here we consider 3connected cubic graphs where two vertices exist so that the three disjoint paths between them contain all of the vertices of the graph (we call these graphs 3*conn ..."
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Cited by 14 (1 self)
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Menger's Theorem states that in a 3connected graph, any two vertices are joined by three openly disjoint paths. Here we consider 3connected cubic graphs where two vertices exist so that the three disjoint paths between them contain all of the vertices of the graph (we call these graphs 3
Shortest Paths in Distanceregular Graphs
 Europ. J. Combinatorics
"... We aim here at introducing a new point of view of the Laplacian of a graph, Γ. With this purpose in mind, we consider L as a kernel on the finite space V (Γ), in the context of the Potential Theory. Then we prove that L is a nice kernel, since it verifies some fundamental properties as maximum and e ..."
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Cited by 13 (7 self)
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obtain the structure of the shortest paths of a distanceregular graph. As a consequence, we find the intersection array in terms of the equilibrium measure. Finally, we give a new characterization of strongly regular graphs. Key words. Distanceregular graph, shortest path, equilibrium potential
Results 1  10
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1,154,818