Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i≠j, dij is the Euclidean distance betwee...Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups.展开更多
文摘Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
文摘Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups.
