This note introduces a quantitative measure (S(G)) of the symmetry structure of a graph G. S(G) is called the index of symmetry of G and is a function of its structural information content and the order of its automorphism group. Properties of S(G) are examined and applications to special classes of graphs are presented. In particular, the index of symmetry of a class of alkanes is shown to be ...

In this paper, an evolutionary clustering technique is described that uses a point symmetry based distance measure. The algorithm is therefore able to detect both convex and non-convex clusters. Kd-tree based nearest neighbor search is used to reduce the complexity of finding the closest symmetric point. The proposed GA with point symmetry distance based (GAPS) clustering technique is compared ...

Skewness indicates a lack of symmetry in a distribution. Knowing the symmetry of the underlying data is important for parametric analysis, fitting distributions or doing transformations to the data. The coefficient of skewness is the commonly used measure to identify a lack of symmetry in the underlying data, although graphical procedures can also be effective. We evaluate five different method...

eight accessions of thyme medicinal plant, belonging to iranian endemic thymus daënensis, t. eriocalyx, t. migricus and an unknown thymus spp species, were tested for karyotypic analysis, using squash technique and 2% (w/v) aceto-orcein staining method. chromosomal parameters examined were: short arm (s), long arm (l), total length of chromosome (tl), arm ratio (ar), r-value, total chromosome v...

Assuming that general intelligence (g) is an honest signal of fitness, we expected g to be related to developmental quality as indexed by Fluctuating Asymmetry (i.e. non-pathological variation in the size of right and left body features). In a population sample of 44 men and 37 women, we assessed the relationship between Fluctuating Asymmetry (FA) and g, and, as a control, to the Big Five perso...

the degree of aromaticity of mono-substituted derivatives of benzene has beeninvestigated using a new index based on electric field gradient index, by using two mechanicalquantum methods with gaussian 03. two different basis sets have applied to study and theresults compared. this strategy has demonstrated that, due to violation of symmetry in have pisystems,how the degree of aromaticity can ha...

The degree of aromaticity of mono-substituted derivatives of benzene has beeninvestigated using a new index based on electric field gradient index, by using two mechanicalquantum methods with Gaussian 03. Two different basis sets have applied to study and theresults compared. This strategy has demonstrated that, due to violation of symmetry in have pisystems,how the degree of aromaticity can ha...

Crystal structures of minerals are defined by a specific atomic arrangement within the unit-cell, which follows laws symmetry to each crystal system. The causes for mineral crystallize in given system have been subject many studies showing their dependency on different formation conditions, such as presence aqueous fluids, biotic activity and others. Different attempts made quantify interpret i...