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Topic: Strongly regular graph

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	Regular graph - Wikipedia, the free encyclopedia
		Regular graph of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of disconnected cycles.
		A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common.
		The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices.
	en.wikipedia.org /wiki/Regular_graph (167 words)

	Comb. Structures: Strongly Regular Graphs
		The complement of a strongly regular graph is strongly regular.
		Pf : Clearly the complement is a regular graph of valency n - k - 1.
		The Gewirtz graph is a strongly regular graph with parameters (56,10,0,2).
	www-math.cudenver.edu /~wcherowi/courses/m6406/srg.html (1606 words)

	Higman-Sims graph
		In the description of the Hoffman-Singleton graph we saw that the Higman-Sims graph is the graph on the 15-cocliques, adjacent when they meet in 0 or 8 points.
		The subgraph induced on the 56 is the Gewirtz graph.
		The subgraph induced on the 20 is the 2-coclique extension of the Petersen graph.
	www.win.tue.nl /~aeb/drg/graphs/Higman-Sims.html (1392 words)

	Encyclopedia: Regular graph
		A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of verticies has the same number n of neighbors in common.
		Eric W. Weisstein, Regular Graph (http://mathworld.wolfram.com/RegularGraph.html) at MathWorld.
		Eric W. Weisstein, Strongly Regular Graph (http://mathworld.wolfram.com/StronglyRegularGraph.html) at MathWorld.
	www.nationmaster.com /encyclopedia/Regular-graph (204 words)

	Pseudo-Random Graphs - Krivelevich, Sudakov (ResearchIndex) (Site not responding. Last check: 2007-11-04)
		Two simple examples of strongly regular graph are the pentagon C 5 that has parameters (5; 2; 0; 1), and the Petersen graph whose parameters are (10; 3; 0; 1).
		Strongly regular graphs were introduced by Bose in 1963 [21] who also pointed out their tight connections with nite geometries.
		As follows from the de nition, strongly regular graphs are highly regular structures, and one can safely predict that...
	citeseer.lcs.mit.edu /592671.html (537 words)

	[No title]
		For identification purposes, a three-dimensional object is represented by an attributed graph describing the geometrical structure and shape of the surface bounding the object.
		Graph Grammars and Their Application to Computer Science}, publisher = {Springer-Verlag}, pages = {174--189}, year = {1990}, abstract = {The paper is concerned with the efficient determination of the set of productions of a graph grammar that are applicable in one rewriting step.
		New graphs can be encoded at run time without recompiling the whole hierarchy: having found a graph's structural type, the authors then use it to hash to the code encoding the poset of all possible type-labeled graphs ordered by subsumption.
	www.ics.uci.edu /~eppstein/bibs/subiso.bib (13928 words)

	U₄(3)
		This graph is the collinearity graph of the unique generalized quadrangle GQ(3,9).
		It is the graph on the vectors of a 4-dimensional vector space over GF(3), where two vectors are adjacent when the quadratic form vanishes on their difference.
		In terms of the graph on the isotropic points the hyperbolic lines are the nonedges (and give a vertex partition 2+10+40+60).
	www.win.tue.nl /~aeb/drg/graphs/U4_3.html (1372 words)

	Strongly Regular Graphs
		Over the years I have been attempting to classify all strongly regular graphs with "few" vertices and have achieved some success in the area of complete classification in two cases that were previously unknown.
		The graphs with parameters (36,15,6,6) all arise in the switching classes of the 227 regular two-graphs that I found in the paper cies above.
		Associated with the (36,15,6,6) graphs are those on 35 vertices obtained by isolating a vertex by switching and deleting it.
	www.maths.gla.ac.uk /~es/srgraphs.html (528 words)

	Hoffman-Singleton graph
		As we saw, Γ is subgraph of the Higman-Sims graph on 100 vertices.
		The graph on the 15-cocliques, adjacent when they meet in 0 or 8 is the Higman-Sims graph.
		The subgraph induced on the orbit of size 30 is Tutte's 8-cage, the incidence graph of the generalized quadrangle GQ(2,2).
	www.win.tue.nl /%7Eaeb/drg/graphs/Hoffman-Singleton.html (917 words)

	05: Combinatorics
		Of course graphs themselves are designs, although it is only the most regular graphs which are included in these discussions.
		A graph is a set V of vertices and a set E of edges -- pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets, which is clearly a broad topic; a more detailed description is available on the index page for Graph Theory.
		Particularly common in the study of strongly regular graphs are association schemes.
	www.math.niu.edu /~rusin/known-math/index/05-XX.html (1988 words)

	A Prolific Construction of Strongly Regular Graphs With the N-E.c. Property - Cameron, Stark (ResearchIndex) (Site not responding. Last check: 2007-11-04)
		A prolific construction of strongly regular graphs with the n-e.c.
		A graph is strongly regular if it is a regular graph such that the number of vertices mutually adjacent to a pair of vertices v 1,v 2 depends only on whether or not } is an edge in the graph.
		6 Hadamard matrices and strongly regular graphs with the - Bonato, Holzmann et al.
	citeseer.lcs.mit.edu /666502.html (513 words)

	www9 paper
		The study of the web as a graph is not only fascinating in its own right, but also yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution.
		Given a directed graph, a strongly connected component (strong component for brevity) of this graph is a set of nodes such that for any pair of nodes u and v in the set there is a path from u to v.
		We refer to the components of the undirected graph obtained from a directed graph by ignoring the directions of its arcs as the weak components of the directed graph.
	www.almaden.ibm.com /cs/k53/www9.final (6311 words)

	Parameters of directed strongly regular graphs: Definition
		A directed strongly regular graph (dsrg) is a (0,1) matrix A with 0's on the diagonal such that the linear span of I, A and J is closed under matrix multiplication.
		In case A is symmetric, we have a strongly regular graph, and that case is excluded here.
		Thus, a directed strongly regular graph cannot be a Cayley graph of an Abelian group.
	homepages.cwi.nl /~aeb/math/dsrg/dsrg-1.html (912 words)

	"Introduction to Graph Theory - new problems"
		Determine whether the graph obtained by deleting a diagonal edge is isomorphic to the graph obtained by deleting one of the edges on the cycle.
		Count the spanning trees in a graph that is the union of a k -cycle and an l -cycle with one common edge.
		Let G be the intersection graph of a finite family of squares in the plane that are translations of a single square.
	www.math.uiuc.edu /~west/igt/newprob.html (8477 words)

	Clearing up the market cycle... best Strongly Connected Graph (Site not responding. Last check: 2007-11-04)
		connected graph is a graph such that there exists a path between all pairs of vertices.
		If the graph is a directed graph, and there exists a path from each vertex to every other vertex, then it is a...
		graph whose underlying graph is connected, and not strongly connected.
	ascot.pl /th/Fourier5/Strongly-Connected-Graph.htm (597 words)

	Show_User (Site not responding. Last check: 2007-11-04)
		One of its formulations: a regular undirected graph is an srg if and only if it has exactly three distinct eigenvalues.
		A more general notion of a directed strongly regular graph (dsrg) was introduced in 1988 by A.M.Duval.
		Our approach to circulant graphs is based on the following methodology: to describe all Schur rings over, to find their automorphism groups and then to use the results for the identification of circulant graphs.
	profiler.bgu.ac.il /site/public_site/Show_User.cfm?user_id=411 (509 words)

	Graph Theory White Pages: Andries E. Brouwer (Site not responding. Last check: 2007-11-04)
		The graphs with spectral radius between 2 and sqrt(2+sqrt(5)).
		A remark on partial linear spaces of girth 5 with an application to strongly regular graphs.
		Distance regular graphs of diameter 3 and strongly regular graphs.
	www.cs.columbia.edu /~sanders/graphtheory/people/Brouwer.AE.html (284 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Introduction Abstract: A regular (undirected) graph of valency k with v vertices is called a strongly regular graph (briefly s.r.g.) if each pair of adjacent vertices has exactly \lambda common neighbors and each pair of non-adjacency vertices has exactly \mu common neighbors.
		The set (v,k,\lambda, \mu) is called the set of main parameters of a strongly regular graph.
		Point graphs of partial geometries will be introduced as one of the important classes of s.r.g.'s.
	www.math.technion.ac.il /~techm/20020515161020020515kli (263 words)

	Directed strongly regular graphs
		A directed strongly regular graph (DSRG) is a graph on n vertices in which every vertex has indegree and outdegree k and the number of paths of length two from a vertex x to a vertex y is t if x=y, $\lambda$ if there is an edge directed from x to y and µ otherwise.
		These graphs were first investigated by A. Duval (1988) and later by M. Klin et al.
		Results on the exact number of non isomorphic graphs are mainly from J1 and J3.
	www.math.aau.dk /~leif/research/dsrg-table.html (271 words)

	Strongly regular graphs
		This is just a list of strongly regular graph parameters for small numbers of vertices to replace the paper copy that I keep losing.
		However as time goes by and I stumble over these graphs or their constructions or whatever, I hope to fill in some of the blank fields left for that purpose.
		If you want to know more about a specific parameter set (for any distance regular graph at all), then you should use the superb program DRG written by Andries Brouwer from the Discrete Mathematics group at the University of Eindhoven.
	www.csse.uwa.edu.au /~gordon/remote/srgs/index.html (316 words)

	Parameters of directed strongly regular graphs: Constructions
		If there exists a srg with parameters v, k, lb, mu, and mu = lb +1, then there is a dsrg with parameters vk, (v - k -1) k, (v - k -1)(k - mu), (v - k -2)(k - mu), (v - k -1)(k - mu).
		If there exists a srg with parameters v, k, lb, mu, and mu = lb, then there is a dsrg with parameters vk, (v - k) k, (v - k)(k - mu), (v - k -1)(k - mu), (v - k)(k - mu).
		Construction: take the edges of the srg, and let xy->uv when u is at distance 0 or 2 from y.
	homepages.cwi.nl /~aeb/math/dsrg/dsrg-2.html (1631 words)

	Clearing up the market cycle... best Strongly Regular Graph (Site not responding. Last check: 2007-11-04)
		In graph theory, a regular regular graph has all vertices of the same valency...
		Strongl y Regular Graph -- from MathWorld Strongly Regular Graph -- from MathWorld A k-regular simple graph G on \nu nodes is strongly k-regular if there exist positive integers k, \lambda, and \mu such that every vertex has k neighbors (i.e.,...
		Directed Strongly Regular Graph -- from MathWorld Directed Strongly Regular Graph -- from MathWorld A directed strongly regular graph is a simple directed graph with adjacency matrix \mathsf{A} such that the span of \mathsf{A}, the identity...
	ascot.pl /th/Fourier5/Strongly-Regular-Graph.htm (574 words)

	Graph Theory White Pages: Alexander Rosa (Site not responding. Last check: 2007-11-04)
		One-factorizations of regular graphs and Howell designs of small order.
		Decomposition of complete graphs into isomorphic factors with a given diameter.
		On the cyclic decompositions of the complete graph into polygons with odd number of edges.
	www.cs.columbia.edu /~sanders/graphtheory/people/Rosa.A.html (185 words)

	Random Strongly Regular Graphs? (ResearchIndex)
		Abstract: Strongly regular graphs lie on the cusp between highly structured and unstructured.
		For example, there is a unique strongly regular graph with parameters (36,10,4,2), but there are 32548 non-isomorphic graphs with parameters (36,15,6,6).
		1 Strongly regular graphs with the n-e (context) - Cameron, Stark
	citeseer.ist.psu.edu /457661.html (437 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Some examples of graphs with cycles of certain even lengths, motivated by the Erdos-Gyarfas conjecture.
		Two vertices of a graph are similar if an automorphism of the graph takes one to the other.
		Strongly regular graph parameters for which the existence question has not been settled.
	ginger.indstate.edu /ge/Graphs (141 words)

	Embedding Arbitrary Finite Simple Graphs Into Small Strongly Regular Graphs. (ResearchIndex)
		Abstract: It is well-known that any finite simple graph \Gamma is an induced subgraph of some exponentially larger strongly regular graph \Gamma (e.g.
		For a given finite simple graph \Gamma on v vertices we present a construction of a strongly regular graph \Gamma on O(v 4) vertices that contains \Gamma as its induced subgraph.
		A discussion is included of the size of the smallest possible strongly regular graph with this property.
	citeseer.ist.psu.edu /31128.html (325 words)

	» Algebraic Graph Theory
		--It is sketchy on chromatic polynomial, planar graph.
		This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general.
		However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory.
	www.mathreading.com /Shop/Algebraic-Graph-Theory/0387952209 (195 words)

	The search for pseudo orthogonal Latin squares of order six (ResearchIndex)
		Abstract: We report on the complete computer search for a strongly regular graph with parameters (36,15,6,6) and chromatic number six.
		1 Introduction Consider a Latin square S of order n.TheLatin square graph #ofS is defined on the entries of S, where two entries are adjacent whenever they are in the same row, in the same column, or carry the same symbol.
		It is well-known and easily verified that if n # 3, # is strongly regular with parameters (n 2, 3(n -...
	citeseer.ist.psu.edu /289310.html (430 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Towards p.d.s.'s on n^2 vertices Abstract: A regular (undirected) graph of valency k with v vertices is called a strongly regular graph (briefly s.r.g.) if each pair of adjacent vertices has exactly \lambda common neighbors and each pair of non-adjacency vertices has exactly \mu common neighbors.
		After that we will start consideration of partial difference sets on n^2 vertices, especially those which are related to Latin squares.
		This is the second lecture in the planning series of a few lectures related to the s.r.g.'s and p.d.s.'s.
	www.math.technion.ac.il /~techm/20020529161020020529kli (235 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Introduction to classical theory Abstract: A regular graph of valency k with v vertices is called a strongly regular graph (briefly s.r.g.) if each pair of adjacent vertices has exactly \lambda common neighbors and each pair of non-adjacency vertices has exactly \mu common neighbors.
		In this lecture I will finish the consideration of a few necessary conditions for a set (v, k, \lambda, \mu) to be the set of the main parameters of a suitable s.r.g.
		This is the fourth lecture in the series of a few introductory lectures related to the theory of s.r.g.'s.
	www.math.technion.ac.il /~techm/19991226171019991226kli (148 words)

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