On the diameter of the intersection graph of a finite simple group

summary:Let $G$ be a finite group. The intersection graph $\Delta _G$ of $G$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of $G$, and two distinct vertices $X$ and $Y$ are adjacent if $X\cap Y\ne 1$, where $1$ denotes the trivial subgroup of order $1$. 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 $28$. In particular, the intersection graph of a finite non-abelian simple group is connected

Graphs as navigational infrastructure for high dimensional data spaces

Data visualization, High dimensional space, Variable graphs, Scatterplot matrices, 2d tours, 3d transition graph, 4d transition graph, Line graphs, Hamiltonians, Hamiltonian decompositions, Graph products, Euler tours, Kneser graph, Space graphs,