Showing papers on "Strongly regular graph published in 1972"
TL;DR: It is shown that every strongly regular normed space admits a representation by means of a projective code, which yields a one-to-one correspondence between two-weight projective codes over prime fields and some strongly regular graphs.
178 citations
TL;DR: Two types of configurations, whose Levi graphs are regular and edge but not vertex transitive, are described and their symmetry is determined in this paper, where the symmetry of these configurations is determined.
83 citations
TL;DR: In this paper, the connection between a strongly regular graph G and a pseudo-geometric graph D(θ0) was studied when the graph G is geometric or pseudogeometric (q2+1,q+1.1,1).
Abstract: Let θ0 be a particular vertex of a strongly regular graph G with parameters v, n1, p
11
1
p
11
1
. Let A be the adjacency matrix of G, and B the submatrix of A whose rows correspond to the vertices of G adjacent to θ0 and whose columns correspond to the vertices of G nonadjacent to θ0. Then the designD(θ0) with incidence matrix B has the parameters v′=n1 b′=v-n1−1, r′=n1−p11/1−1, k′ = p
11
2
. In this paper we study the connection between G andD(θ0) when the graph G is geometric or pseudo-geometric (q2+1,q+1,1).
41 citations
IBM1
TL;DR: In this article, the relationship between geometric properties of a graph and the spectrum of its adjacency matrix was studied and lower bounds for α, β, γ were given in terms of the spectrum.
37 citations
TL;DR: In this paper, a formula is developed to give the genus for a large class of lexicographic products, which is the minimum genus among all closed orientable 2-manifolds M in which G can be imbedded.
Abstract: Given two graphs G and H, a new graph G(H), called the composition (or lexicographic product) of G and H, can be formed. In this paper, a formula is developed to give the genus for a large class of lexicographic products. In the simplest special case, the genus of the product is given by the first Betti number of one of the factors. In the present context, a graph is a finite 0- or 1- complex. For terms not defined below, see [2] and [6]. The genus, Ύ(G), of a graph G is the minimum genus among the genera of all closed orientable 2-manifolds M in which G can be imbedded. An imbedding of G in M is said to be minimal if M has genus Ύ(G). The first Betti number, β(G), of a graph G is given by β(G) = q — p + k, where G has q edges, p vertices, and k components; β(G) counts the number of independent cycles in G. Given two graphs G and H with disjoint vertex sets V(G), V(H) and edge sets E(G), E(H) respectively, the composition (or lexicographic product) G(H) has vertex set given by the cartesian product V(G) x V(H), with two vertices {u^ vά) and (uk, vm) adjacent in G(H) if and only if either: (i) ut = uk and vάvm is in E(H), or (ii) u-uk is in E(G). For example, the regular complete m-partite graph on mn vertices is just the composition Km(Kn), where Ks denotes the complete graph on s vertices,
24 citations
TL;DR: The purpose of this paper is to find a necessary and sufficient condition for the existence of a decomposition of a complete graph with given number of vertices into regular bichromatic factors and to answer the question what is the possible number of factors in such a decompose.
7 citations