Related papers: On intriguing sets in five classes of strongly reg…
In this paper, we classify the groups of semisimilarities of finite classical polar spaces with exactly two orbits on the singular or isotropic points. As a byproduct, we obtain many highly symmetric regular sets in the point graphs of…
We describe a general construction of strongly regular graphs from the collinearity graph of a finite classical polar spaces of rank at least $3$ over a finite field of order $q$. We show that these graphs are non-isomorphic to the…
We construct an infinite family of intriguing sets that are not tight in the Grassmann Graph of planes of PG$(n,q)$, $n\ge 5$ odd, and show that the members of the family are the smallest possible examples if $n\ge 9$ or $q\ge 25$.
We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type $U(n, 2)$, $O(n, 3)$, $O(n, 5)$, $O^+(n, 3)$, and $O^-(n, 3)$ are not determined by its parameters for $n \geq 6$. We prove this by…
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…
In this paper, we determine all connected net-regular strongly regular signed graphs with degree 5. There are five and two strongly regular signed graphs with net-degree 3 and 1, respectively.
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 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).
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…
We study here the graphs with seven vertices in an effort to classify which of them appear as the prime character degree graphs of finite solvable groups. This classification is complete for the disconnected graphs. Of the 853…
We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomial.
We consider various regular graphs defined on the set of elements of given rank of a finite polar space. It is likely that no two such graphs, of the same kind but defined for different ranks, can have the same degree. We shall prove this…
We investigate prime character degree graphs of solvable groups that have six vertices. There are one hundred twelve non-isomorphic connected graphs with six vertices, of which all except nine are classified in this paper. We also…
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…
Classification of planar unit-distance graphs with up to 9 edges, by homeomorphism and isomorphism classes. With exactly nine edges, there are 633 nonisomorphic connected matchstick graphs, of which 196 are topologically distinct from each…
We survey the area of strongly regular graphs satisfying the 4-vertex condition and find several new families. We describe a switching operation on collinearity graphs of polar spaces that produces cospectral graphs. The obtained graphs…
In this paper, an effort is made to classify which prime character degree graphs having eight vertices occur for some finite solvable group. To approach this, we compile known results and constructions from the literature which are used to…
In this paper, we study the net-regular strongly regular signed graphs with degree 6 and determine all connected 6-regular and net-regular strongly regular signed graphs. There are three, six and four 6-regular strongly regular signed…
In this paper, we study association schemes on the anisotropic points of classical polar spaces. Our main result concerns non-degenerate elliptic and hyperbolic quadrics in PG$(n,q)$ with $q$ odd. We define relations on the anisotropic…