it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

In 2005, Exoo posed the following question. Fix $\epsilon$ with $0\leq\epsilon<1$. Let $G_\epsilon$ be graph whose vertex set is Euclidean plane, where two vertices are adjacent iff distance between them lies in closed interval $[1-\epsilon,1+\epsilon]$. What chromatic number $\chi(G_\epsilon)$ of this graph? The case $\epsilon=0$ precisely classical ``chromatic plane'' problem. a 2018 p...