Computational Techniques for the Automorphism Groups of Graphs

Balasubramanian, K.

doi:10.1021/ci00019a022

Cited by 18 publications

(13 citation statements)

References 19 publications

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“…and/or 4!. Possible values for α > 1 are therefore 2,4,6,8,12,16,24,32,36,48,64,72,96,128,144,192,216,256,288,384,432,512,576,768,1024, and so on. The limited number of different values of α restricts the use of molecular descriptors that are based only on α.…”

Section: Theory and Methodsmentioning

confidence: 99%

“…The complete information about constitutionally equivalent atoms and bonds is contained in the data of the automorphism group of a graph representing the molecular structure. [4][5][6] Automorphism means mapping of a graph onto itself while preserving the connectivity (not cutting any bonds). Asymmetric structures have only a single mapping -the trivial identity mapping -while for highly symmetric structures several (sometime many) mappings onto itself exist.…”

Section: Introductionmentioning

confidence: 99%

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Automorphism Groups of Alkane Graphs

et al. 2021

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The complete set of 618047 isomers of the alkanes with 4 to 20 carbon atoms has been created. From all isomers the automorphism groups have been calculated and evaluated in terms of size, number of asymmetric carbon atoms, and numeric properties of atom and bond orbits. The presence of a symmetric bond is related to the number of atom and bond orbits. Molecular descriptors based on automorphism data have been studied, including the known symmetry index, an entropy measure and the root of an orbit polynomial. These descriptors are closely related to the presence of symmetric substructures. The prediction performance of QSPR models for three molecular properties of alkanes and using binary substructure descriptors, is improved by adding descriptors based on automorphism data.

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Section: Theory and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Automorphism Groups of Alkane Graphs

et al. 2021

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“…This group is valuable for the studying of chemical structures, as seen in [2]. Also, algorithms have been designed to determine these groups for particular graphs (see [1] and [5]).…”

Section: Definitionmentioning

confidence: 99%

Structural Equivalence in Graphs and Complete Skeletons

Higgins¹

2020

Preprint

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Two vertices u and v of a graph Γ are strucuturally equivalent if and only if the transposition (u v) is in Aut(Γ), the automorphism group of Γ. Some properties of structural equivalence and the group of vertex permutations generated by the transpositions in Aut(Γ) are discussed, along with the prime graphs of these groups. The notion of structural equivalence is used to develop a way of reconfiguring graphs into what are called their complete skeletons, which is closely related to compression graphs. Finally, the complete skeleton of a graph Γ, denoted Ω(Γ), is used to find a formula for rank(I + A(Γ)), which is helpful for determining the multiplicity of the -1 eigenvalue of Γ.

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“…Symmetry, as one of the important properties for graph filtering, is also an essential factor in characterizing and measuring complex networks [14,15] as demonstrated in Conder [16] who organized a series of highly symmetric graphs. Automorphism group directly represents graph symmetry, the computation of which has been extensively studied [17] and applied in structural modeling and design [18,19]. The rest of this paper introduces, in Sec.…”

Section: Introductionmentioning

confidence: 99%