相关论文: On the existence of directed strongly regular grap…
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…
In this paper we present a method for constructing directed strongly regular graphs with assumed action of an automorphism group. The application of this method leads to first examples of directed strongly regular graphs with parameters…
In this paper, we prove the existence of directed strongly regular graphs with parameters $(63,11,8,1,2)$. We construct a pair of nonisomorphic dsrg(63,11,8,1,2), where one is obtained from the other by reversing all arrows. Both directed…
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…
We construct a strongly regular graph with the parameters (65; 32; 15; 16). The idea is to search for an adjacency matrix that consists of circulant blocks. Equations with such matrices can be reduced to congruences with polynomials…
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…
In this paper, we introduce orbit matrices of directed strongly regular graphs (DSRGs). Further, we propose a method of constructing directed strongly regular graphs with prescribed automorphism group using genetic algorithm. In the…
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…
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 investigate the automorphism group of the substructure ordering of finite directed graphs. The second author conjectured that it is isomorphic to the 768-element group $(\mathbb{Z}_2^4 \times S_4)\rtimes_{\alpha} \mathbb{Z}_2$. Though…
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,…
In this paper, we characterize some certain directed strongly regular Cayley graphs on Dihedral groups $D_{n}$, where $n\geqslant 3$ is a positive integer.
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…
An explicit construction of infinite sequences of strongly regular digraphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, \lambda, t)$ is described. A computer program was used to find the initial digraphs. The remaining…
We consider orbit partitions of groups of automorphisms for the symplectic graph and apply Godsil-McKay switching. As a result, we find four families of strongly regular graphs with the same parameters as the symplectic graphs, including…
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
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.…
A new family of strongly regular graphs, called the general symplectic graphs $Sp(2\nu, q)$, associated with nonsingular alternate matrices is introduced. Their parameters as strongly regular graphs, their chromatic numbers as well as their…
We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley…
Twelve new strongly regular graphs with parameters (81,30,9,12) are found as graphs invariant under certain subgroups of the automorphism groups of the two previously known graphs that arise from 2-weight codes. One of these new graphs is…