2,608 research outputs found
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 in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Some properties of the Hoffman-Singleton graph
The Hoffman-Singleton graph, with spectrum 7(1), 2(28), -3(21), is characterized among regular graphs by a star complement for the eigenvalue 2, that is, by an induced subgraph of order 22 without 2 as an eigenvalue. Properties of other induced subgraphs are noted; in particular, the subgraph induced by vertices at distance 2 from a given vertex is the edge-disjoint union of three Hamiltonian cycles.peer-reviewe
Distance-regular graph with large a1 or c2
In this paper, we study distance-regular graphs that have a pair of
distinct vertices, say x and y, such that the number of common neighbors of x
and y is about half the valency of . We show that if the diameter is at
least three, then such a graph, besides a finite number of exceptions, is a
Taylor graph, bipartite with diameter three or a line graph.Comment: We submited this manuscript to JCT
The Gewirtz graph: An exercise in the theory of graph spectra
Graphs;mathematics
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