Related papers: On strongly regular graph with parameters (65; 32;…
In this paper, we give a complete description of strongly regular graphs with parameters ((n^2+3n-1)^2,n^2(n+3),1,n(n+1)). All possible such graphs are: the lattice graph $L_{3,3}$ with parameters (9,4,1,2), the Brouwer-Haemers graph with…
In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The construction produces strongly regular graphs with the same…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
We characterize the graphs with loops whose degree sequences have no repeated values and find their adjacency spectrum. In the case of simple graphs, such graphs are called anti-regular graphs and are examples of threshold graphs. The…
A quasi-strongly regular graph of grade $p$ with parameters $(n, k, a; c_1, \ldots, c_p)$ is a $k$-regular graph of order $n$ such that any two adjacent vertices share $a$ common neighbours and any two non-adjacent vertices share $c_{i}$…
We determine new upper bounds for the clique numbers of strongly regular graphs in terms of their parameters. These bounds improve on the Delsarte bound for infinitely many feasible parameter tuples for strongly regular graphs, including…
We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the…
We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…
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…
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…
We provide an abundance of strongly regular graphs (SRGs) for certain parameters $(n, k, \lambda, \mu)$ with $n < 100$. For this we use Godsil-McKay (GM) switching with a partition of type $4,n-4$ and Wang-Qiu-Hu (WQH) switching with a…
We give two constructions of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new…
We address the problem of constructing large undirected circulant networks with given degree and diameter. First we discuss the theoretical upper bounds and their asymptotics, and then we describe and implement a computer-based method to…
We study functional graphs generated by quadratic polynomials over prime fields. We introduce efficient algorithms for methodical computations and provide the values of various direct and cumulative statistical parameters of interest. These…
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 construct a new family of strongly regular graphs with the same parameters as the strongly regular graphs $D_{5,5}(q)$. The construction can be seen as a variant of the construction of twisted Grassmann graphs by Van Dam and Koolen.
In this article we construct a series of new infinite families of strongly regular graphs with the same parameters as the point-graphs of non-singular quadrics in PG(n,2).
A normally regular digraph with parameters $(v,k,\lambda,\mu)$ is a directed graph on $v$ vertices whose adjacency matrix $A$ satisfies the equation $AA^t=k I+\lambda (A+A^t)+\mu(J-I-A-A^t)$. This means that every vertex has out-degree $k$,…
Over forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph $X$ contains a Hadamard matrix then $X$ is either of Latin square type or of negative Latin square type. We extend their result to…