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Symmetry Properties of Some Chemical Graphs

Croatian International Relations Review

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Title Symmetry Properties of Some Chemical Graphs
Simetrijska svojstva nekih kemijskih grafova
 
Creator Ashrafi, Ali Reza
Hamadanian, Masood
 
Subject weighted graph; Euclidean graph; trimethylamine; cubane
 
Description Let G be a weighted graph with the adjacency matrix A = [aij]. A Euclidean graph associated with a molecule is defined by a weighted graph with the 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 to be zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian computed the Euclidean graphs and 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). The present work describes a simple computational method by means of which it is possible to calculate the automorphism group of weighted graphs. We have applied this method to compute the symmetry of trimethylamine and cubane.
Neka je G uteženi graf s matricom susjedstva A = [aij]. Euklidski graf pridružen molekuli definiran je kao uteženi graf s matricom susjedstva D = [dij], gdje je dij euklidska udaljenost između čvorova i i j. U toj matrici dijagonalni elementi dii jednaki su nuli, ako su svi čvorovi grafa ekvivalentni. Ako nisu, tada se uvode težine za različite čvorove. Balasubramanian je izračunao euklidske grafove i grupe automorfizama benzena, otkrivene i zasjenjene konformacije etana i ferocena (vidi Chem. Phys. Lett. 232 (1995) 415–423). U ovome radu je prikazana jednostavna računska metoda pomoću koje se mogu računati grupe automorfizama za utežene grafove. Metoda je ilustrirana na računanju simetrijskih svojstava grafova kojima su prikazani trimetilamin i kuban.
 
Publisher Croatian Chemical Society
 
Date 2005
 
Type text
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
 
Format application/pdf
 
Identifier https://hrcak.srce.hr/6
https://hrcak.srce.hr/file/6
 
Source Croatica Chemica Acta
ISSN 0011-1643 (Print)
ISSN 1334-417X (Online)
Volume 78
Issue 2
 
Language eng
 
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