Thesis (Ph.D.) - University of Birmingham, Dept of Pure Mathematics.
The point graph of the geometry. Each precisely 4-isoregular graph is a pseudogeometric graph. An amply regular graph with certain We prove that a strongly regular graph Γ with parameters. The graphs C a y (F p 2 ℓ s, D i), 1 ⩽ i ⩽ p ℓ + 1, are all negative Latin square type or all Latin square type strongly regular graphs according as s is even or odd. Then, C a y (F p 2 ℓ (s + 1) × F p 2 ℓ s, D) is a negative Latin square type strongly regular graph, where D = ⋃ i = 1 p ℓ Cited by: 2. The Paley graphs and other strongly regular (and similar) graphs have been used as models of \pseudo-random graphs" (see Thomason ). Recently, Fon-Der-Flaass  has observed that an old construction of Wallis  gives rise to more than exponentially many strongly regular graphs with various parameter sets to be discussed below. An approach to the enumeration of feasible parameters for strongly regular graphs is described, based on the pair of structural parameters (a,c) and the positive eigenvalue e.
Book description. The projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, . Note that any rank 3 graph is a strongly regular graph. The converse is not always true. The complementary graph of a strongly regular graph with parameters (n,k,λ,µ) is a strongly regular graph with parameters (n,n− k − 1,n−2k + µ− 2,n−2k +λ). A code CG of a graph G is the code of its (0,1)-adjacency matrix. The dimension of CG. A new partial geometry with parameters (s,t,α) = (7,8,4), J. Geometry 16 () K. Coolsaet, некоторых классов сильно регулярных графов = The construction and properties of certain classes of strongly regular graphs (Russian), Uspehi Mat. Tomorrow's answer's today! Find correct step-by-step solutions for ALL your homework for FREE!
To keep things short I skip some definitions on strongly-regular graphs. All necessary information is contained in the paper (see section on strongly-regular graphs). Bondarenko uses a representation of strongly regular graphs to construct a two-distance set in a dimension. We survey the relationships between two-weight linear (n, k) codes over GF(q), projective (n, k, /»" /»,) sets in PG(£— \,q), and certain strongly regular graphs. We also describe and. Strongly regular graphs. A graph X is strongly regular with parameters (n, k, λ, μ) if X has n vertices, every vertex has degree k, each pair of adjacent vertices has λ common neighbors, and each pair of non-adjacent vertices has μ common neighbors. The complement of a SR graph is SR, so we may always assume k ≤ (n − 1) / 2. 3. A Strongly Regular Graph Derived from the Perfect Ternary Golay Code 4. Characterization Problems of Combinatorial Graph Theory 5. Line-Minimal Graphs with Cyclic Group 6. Circle Geometry in Higher Dimensions 7. Bose as Teacher—The Early Years 8. Construction of Symmetric Hadamard Matrices 9. Cayley Diagrams and Regular Complex Polygons