. . These are (a) (29,14,6,7) and (b) (40,12,2,4). Contents 1 Graphs 1 1.1 Stronglyregulargraphs . 1. (10,3,0,1), the 5-Cycle (5,2,0,1), the Shrikhande graph (16,6,2,2) with more. So a srg (strongly regular graph) is a regular graph in which the number of common neigh-bours of a pair of vertices depends only on whether that pair forms an edge or not). Database of strongly regular graphs¶. . In graph theory, a discipline within mathematics, a strongly regular graph is defined as follows. Of these, maybe the most interesting one is (99,14,1,2) since it is the simplest to explain. STRONGLY REGULAR GRAPHS Throughout this paper, we consider the situation where r and A are a com- plementary pair of strongly regular graphs on a vertex set X of cardinality n, with (1, 0) adjacency matrices A and B, respectively. . ... For all graphs, we provide statistics about the size of the automorphism group. Strongly Regular Graphs (This material is taken from Chapter 2 of Cameron & Van Lint, Designs, Graphs, Codes and their Links) Our graphs will be simple undirected graphs (no loops or multiple edges). . Nash-Williams, Crispin (1969), "Valency Sequences which force graphs to have Hamiltonian Circuits", University of Waterloo Research Report, Waterloo, Ontario: University of Waterloo Search nearly 14 million words and phrases in more than 470 language pairs. . Every two non-adjacent vertices have μ common neighbours. . We consider the following generalization of strongly regular graphs. A directed strongly regular graph is a simple directed graph with adjacency matrix A such that the span of A, the identity matrix I, and the unit matrix J is closed under matrix multiplication. 2. It is known that the diameter of strongly regular graphs is always equal to 2. We also find the recently discovered Krčadinac partial geometry, therefore finding a third method of constructing it. . . strongly regular). . . Strongly Regular Graphs on at most 64 vertices. . Eric W. Weisstein, Regular Graph en MathWorld. The all 1 vector j is an eigenvector of both A and J with eigenvalues k and n respectively. . strongly regular graphs on less than 100 vertices for which the existence of the graph is unknown. We say that is a strongly regular graph of type (we sometimes write this as ) if it satisfies all of the following conditions: . This module manages a database associating to a set of four integers \((v,k,\lambda,\mu)\) a strongly regular graphs with these parameters, when one exists. Translation for: 'strongly regular graph' in English->Croatian dictionary. A strongly regular graph is called imprimitive if it, or its complement, is discon- nected, and primitive otherwise. Both groupal and combinatorial aspects of the theory have been included. Graphs do not make interesting designs. . We recall that antipodal strongly regular graphs are characterized by sat- C4 is strongly regular with parameters (4,2,0,2). . common neighbours. 2. A graph is said to be regular of degree if all local degrees are the same number .A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, and a two-regular graph consists of one or more (disconnected) cycles. Draft, April 2001 Abstract Strongly regular graphs form an important class of graphs which lie somewhere between the highly structured and the apparently random. . . . . . . El gráfico de Paley de orden 13, un gráfico fuertemente regular con parámetros srg (13,6,2,3). . . . graphs (i.e. For strongly regular graphs, this has included an 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. . Applying (2.13) to this vector, we obtain A regular graph is strongly regular if there are two constants and such that for every pair of adjacent (resp. Eric W. Weisstein, Strongly Regular Graph en MathWorld. Spectral Graph Theory Lecture 24 Strongly Regular Graphs, part 2 Daniel A. Spielman November 20, 2009 24.1 Introduction In this lecture, I will present three results related to Strongly Regular Graphs. . Strongly Regular Graph. non-adjacent) vertices there are (resp. ) . is a -regular graph, i.e., the degree of every vertex of equals . . . Imprimitive strongly regular graphs are boring. There are some rank 2 finite geometries whose point-graphs are strongly regular, and these geometries are somewhat rare, and beautiful when they crop up (like pure mathematicians I guess). Strongly regular graphs are extremal in many ways. 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