Let $ k\geq 1$ be an odd integer, ${t=\left\lfloor {\tfrac {{k+ 2}}{4}}\right\rfloor} $, and q be a
prime power. We construct a bipartite, q-regular, edge-transitive graph $ CD (k, q) $ of order $\…

The non-commuting graph of a finite group G is a highly symmetrical object (indeed, embeds
in ), yet its complexity pales in comparison to that of G. Still, it is natural to seek conditions …

Let S denote an orientablesurface of least genus on which the finite group G acts in an
effective and orientation-preserving manner. We define the genus g (G) of the group G to bethe …

We study the graphs D(k,q) of [4] with particular emphasis on their connected components
when q is odd. In [6] the authors proved that these components (most often) provide the best-…

In [lo] the author determines which sporadic groups other than Fizz, Fz3, Fb4, Th, J4, B, and
M are Hurwitz groups, ie, generated by elements x and y with order (x)= 2, order (y)= 3, and …

Let C 2k be the cycle on 2k vertices, and let ex(v, C 2k ) denote the greatest number of edges
in a simple graph on v vertices which contains no subgraph isomorphic to C 2k . In this …

A group G is said to be 3/2-generated if, given an arbitrary non-identity element x of G one
can always find an element y= y (x) of G such that (x, y)= G. We refer to such an element y as …

… In [12], Lazebnik, Ustimenko and Woldar showed that the graphs D(n, q) are disconnected
for n … , bi0j0 v2i0 , as otherwise K would be a cycle in either C or Hij for some i, j. But now the …

In this paper we present a simple method for constructing infinite families of graphs defined
by a class of systems of equations over commutative rings. We show that the graphs in all …

A set M of nonzero integers is said to split a finite abelian group G if there is a subset S of G
for which $ M\cdot S= G\backslash\{0\} $. If, moreover, each prime divisor of $| G| $ divides an …