On strongly homogeneous tournaments
On Subgroups Generated by a Root Triple.
On suborbital graphs for the normalizer of .
On Symmetric and Antisymmetric Relations.
On the automorphism group of an infinite graph.
On the automorphism group of integral circulant graphs.
On the composition factors of a group with the same prime graph as
Let be a finite group. The prime graph of is a graph whose vertex set is the set of prime divisors of and two distinct primes and are joined by an edge, whenever contains an element of order . The prime graph of is denoted by . It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if is a finite group such that , where , then has a unique nonabelian composition factor isomorphic to or .
On the Corona of Two Graphs.
On the Corona of Two Graphs. (Short Communication).
On the determining number and the metric dimension of graphs.
On the diameter of the intersection graph of a finite simple group
Let be a finite group. The intersection graph of is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of , and two distinct vertices and are adjacent if , where denotes the trivial subgroup of order . A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters of intersection...
On the energy of unitary Cayley graphs.
On the function “sandwiched" between and .
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