Titlebook: Mathematical Concepts in Organic Chemistry; Ivan Gutman,Oskar E. Polansky Textbook 1986 Springer-Verlag Berlin Heidelberg 1986 algebra.che

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Some Interrelations between Symmetry and Automorphism Groupsatoms about their mean positions are discussed in terms of . (see paragraph 8.4.3). This concept begins to break down when an internal degree of freedom (e.g. the torsion of a methyl group) becomes fully excited. As the shall show later, automorphism groups of the molecular graph are well-suited to treat the symmetry in non-rigid molecules.

Sinus-Rhythm

歡呼

Fundamentals of Graph Theoryf molecular graphs. The present chapter will, finally, provide a precise mathematical characterization of a graph. We shall list here a number of additional graph-theoretical definitions and mention a few basic properties of graphs.

最初

Graph Theory and Molecular Orbitalsmolecules. The wave function for a .-electron is presented in the LCAO form . where {.> symbolizes a .-vorbital located on the .-th atom of the conjugated molecule, and the summation goes over all . atoms which participate in the conjugation.

財政

Topological Indicesthe information contained in the molecular graph into a numerical characteristic. Every number which is uniquely determined by a graph is called a graph invariant. Those invariants of molecular graphs which are used for structure-property or structure-activity correlations are usually called topological indices (of the corresponding molecule).

尾隨

Topological Aspects in ChemistrySince the time of ., chemists are used to thinking about molecules as geometric objects in which atoms have a certain spatial arrangement. The geometric parameters of molecules (interatomic distances, bond angles, dihedral angles, etc.) can be measured with a rather high degree of accuracy and are indeed known in a considerable number of cases.

上釉彩

emission

Special Molecular GraphsIn graph theory a connected acyclic graph is called a tree. Hence we may say that the topology of acyclic molecules is represented by trees; the essential topological properties of acyclic molecules coincide with those of trees. In the following we shall get acquainted with the basic properties of trees.

Arresting

Fundamentals of Group TheoryGroups are sets of elements amended with a combination law that satisfies certain conditions (axioms).