Symmetries of weighted complete graphs of tetranitrocubane and octanitrocubane

An Euclidean graph associated to a molecule is defined by a weighted graph with the adjacency matrix D = [d(ij)], where d(ij) is the Euclidean distance between the nuclei i and j. Balasubramanian computed the Euclidean graphs and its automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene (see Chem. Phys. Letters 232(1995), 415-423). In this work using the D-4 geometry of octanitrocubane (ONC) and D-2 geometry of tetranitrocubane (TNC), which are essentially the same as the conformation found in crystal states, the distance matrices of ONC and TNC are computed. Then using GAP, the automorphism group of weighted graphs related to tetranitrocubane and octanitrocubane are calculated.