21 research outputs found
Decompositions of complete bipartite and tripartite graphs into selfcomplementary factors with finite diameters
We completely determine the spectrum of the complete bipartite and tripartite graphs that are decomposable into two isomorphic factors with a finite diameter
On the diameter of the intersection graph of a finite simple group
summary: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 graphs of finite non-abelian simple groups have an upper bound . In particular, the intersection graph of a finite non-abelian simple group is connected