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Distance-Regular Graphs
TLDR
In this paper, a connected simple graph with vertex set X of diameter d is considered, and the authors define Ri X2 by (x, y) Ri whenever x and y have graph distance.Abstract:
Consider a connected simple graph with vertex set X of diameter d. Define Ri X2 by (x, y) Ri whenever x and y have graph distanceread more
Citations
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Journal ArticleDOI
On pseudo-distance-regularity
TL;DR: In this article, some properties of locally pseudo-distance-regular graphs are studied and some new characterizations of such structures are also derived, where the concept of local pseudo-regularity is introduced as a natural generalization of distance regularity.
Journal ArticleDOI
An algorithmic approach to fundamental groups and covers of combinatorial cell complexes
Sarah Rees,Leonard H. Soicher +1 more
TL;DR: A practical algorithmic approach to the computation of fundamental groups and first homology groups (as finitely presented groups), of firsthomology groups mod p(as vector spaces), of deck groups ( as permutation groups), and of covers of finite simple such complexes.
Journal ArticleDOI
A Family of Antipodal Distance-Regular Graphs Related to the Classical Preparata Codes
TL;DR: In this paper, a new family of distance-regular graphs is constructed, which are antipodal 22t−1-fold covers of the complete graph on 22t vertices.
Journal ArticleDOI
Independent Sets In Association Schemes
Chris Godsil,M. W. Newman +1 more
TL;DR: This paper shows how the bound α(X) can be used to characterise the maximal independent sets in certain classes of graphs and shows that a graph defined on the partitions of {1, . . . ,9} with three cells of size three is a core.
Journal ArticleDOI
Distance-regular graphs with a1 or c2 at least half the valency
Jack H. Koolen,Jongyook Park +1 more
TL;DR: It is shown 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.
References
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Journal ArticleDOI
Equilateral point sets in elliptic geometry
J.H. van Lint,J.J. Seidel +1 more
TL;DR: In this paper, the authors highlight equilateral point sets in elliptic geometry and show that Paley's construction may be reversed to obtain a C -matrix of order 46, in view of the existence of a Hadamard matrix of order 92.
BookDOI
On construction and identification of graphs
TL;DR: The problem of graph identification has been studied in the theory of permutation groups for a long time, see as mentioned in this paper for a discussion of the main points of the problem and an algorithm for graph identification.