On the graphs of Hoffman-Singleton and Higman-Sims.
On the intersection graph of a commutative distributive groupoid
On the intersection graph of a finite group
For a finite group , the intersection graph of which is denoted by is an undirected graph such that its vertices are all nontrivial proper subgroups of and two distinct vertices and are adjacent when . In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of .
On the intersection graphs of ideals of direct product of rings
In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.
On the intersection of subgroups of a free group.
On the isoperimetry of graphs with many ends
Let X be a connected graph with uniformly bounded degree. We show that if there is a radius r such that, by removing from X any ball of radius r, we get at least three unbounded connected components, then X satisfies a strong isoperimetric inequality. In particular, the non-reduced -cohomology of X coincides with the reduced -cohomology of X and is of uncountable dimension. (Those facts are well known when X is the Cayley graph of a finitely generated group with infinitely many ends.)
On the maximum automorphism group of self-complementary graphs
On the noncommuting graph associated with a finite group.
On the number of representations of an element in a polygonal Cayley graph
We compute explicitly the number of paths of given length joining two vertices of the Cayley graph of the free product of cyclic groups of order k.
On the prime graphs of the automorphism groups of sporadic simple groups
In this paper as the main result, we determine finite groups with the same prime graph as the automorphism group of a sporadic simple group, except .
On the proof of a theorem of Pálfy.
On the spectrum of the derangement graph.
On the unitary Cayley graph of a finite ring.
On Tits' conjecture and other questions concerning Artin and generalized Artin groups.
On wsq-primary ideals
We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let be a commutative ring with a nonzero identity and a proper ideal of . The proper ideal is said to be a weakly strongly quasi-primary ideal if whenever for some , then or Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional...
Parastrophically Equivalent Quasigroup Equations
Partial line graph operator and half-arc-transitive group actions
Percolation on nonamenable products at the uniqueness threshold
Perfect Codes in Antipodal Distance-Transitive Graphs.
Polarities of G. Higman's symmetric design and a strongly regular graph on 176 vertices.