Related papers: On strongly regular graph with parameters (65; 32;…
The paper shows the existence of a family of directed strongly regular graphs with parameters (22, 9, 6, 3, 4). The adjacency matrices of the found digraphs are composed of $3\times 3$ circulant blocks. The automorphism group of all the…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
In this paper we construct all strongly regular graphs, with at most 600 vertices, admitting a transitive action of the orthogonal group $O^+(6,2)$ or $O^-(6,2)$. Consequently, we prove the existence of strongly regular graphs with…
Strongly regular graphs are highly symmetrical and can be described fully with just a few parameters yet the existence of many of them is still under the question. Due to this uncertainty, it is of immense interest to study their structure,…
We prove the existence of directed strongly regular graphs with parameters (60,21,11,6,8), (60,22,12,8,8), (60,24,10,9,10), (60,25,17,8,12), (60,27,21,12,12) and (60,28,20,14,12). The group $S_5 \times 2$ acts transitively on the…
The paper constructs an infinite sequence of strongly regular directed graphs. The construction is based on representing adjacency matrices as block matrices composed of circulant blocks, together with the use of a compactification…
We consider simple loopless finite undirected graphs. Such a graph is called strongly regular with parameter set (v,k,l,m), for short a srg(v,k,l,m), iff it has exactly v vertices, each of them has exactly k neighbours, and the number of…
The graph $G$ is said to be strongly regular with parameters $(n,k,\lambda,\mu)$ if the following conditions hold: (1) each vertex has $k$ neighbours; (2) any two adjacent vertices of $G$ have $\lambda$ common neighbours; (3) any two…
The concept of directed strongly regular graphs was introduced by Duval in his paper, A Directed Graph Version of Strongly Regular Graphs. Duval also provided several construction methods for directed strongly regular graphs. The directed…
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. The Krein bound ensures that there are only finitely many…
Strongly regular graphs are regular graphs with a constant number of common neighbours between adjacent vertices, and a constant number of common neighbours between non-adjacent vertices. These graphs have been of great interest over the…
We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs…
This is a report on a failed attempt to construct new graphs that are strongly regular with no triangles. The approach is based on the assumption that the second subconstituent has an equitable partition with four parts. For infinitely many…
We investigate the second smallest unresolved feasible set of parameters of strongly regular graphs, $(v,k,\lambda,\mu)=(85,14,3,2)$. Using the classification of cubic graphs of small degree, we restrict possible local structure of such a…
Strongly regular graphs (SRGs) are highly symmetric combinatorial objects, with connections to many areas of mathematics including finite fields, finite geometries, and number theory. One can construct an SRG via the Cayley Graph of a…
The symplectic graph Sp(2d, q) is the collinearity graph of the symplectic space of dimension 2d over a finite field of order q. A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1, lambda_2 ,m,n) if…
The paper provides the first constructions of strongly regular graphs and association schemes from weakly regular plateaued functions over finite fields of odd characteristic. We generalize the construction method of strongly regular graphs…
Duval, in "A Directed Graph Version of Strongly Regular Graphs" [{\it Journal of Combinatorial Theory}, Series A 47 (1988) 71 - 100], introduced the concept of directed strongly regular graphs. In this paper we construct several rich…
In this paper, we generalize the construction of strongly regular graphs in [Y. Tan et al., Strongly regular graphs associated with ternary bent functions, J. Combin.Theory Ser. A (2010), 117, 668-682] from ternary bent functions to $p$-ary…
A result of Erd\"os and R\'enyi shows that for a fixed integer n almost all graphs satisfy the n-e.c. adjacency property. However, there are few explicit constructions of n e.c. graphs for n > 2, and almost all known families of n-e.c.…