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By R. Bruce King

Functions of Graph thought and Topology in Inorganic Cluster and Coordination Chemistry is a text-reference that gives inorganic chemists with a rudimentary wisdom of topology, graph conception, and similar mathematical disciplines. The booklet emphasizes the appliance of those themes to steel clusters and coordination compounds.

The book's preliminary chapters current history info in topology, graph thought, and team idea, explaining how those subject matters relate to the houses of atomic orbitals and are utilized to coordination polyhedra. next chapters observe those principles to the constitution and chemical bonding in different different types of inorganic compounds, together with boron cages, steel clusters, strong country fabrics, steel oxide derivatives, superconductors, icosahedral stages, and carbon cages (fullerenes). The book's ultimate bankruptcy introduces the applying of topology and graph idea for learning the dynamics of rearrangements in coordination and cluster polyhedra.

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Additional info for Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry

Example text

Biggs, Finite Groups o f Automorphisms, Cambridge University Press, London, 1971. 6 28 Applications of Graph Theory and Topology obviously the highest symmetry permutation group of degree n. All permutation groups of degree n must be a subgroup of the corresponding symmetric group Pn. Let us now consider the permutation group structure of the permutations of ligands attached to a polyhedral skeleton, such as in a metal complex of the stoichiometry MLnJ A permutation Pnof n objects can be described by a 2 x n matrix of the general type (2-4) In the example of interest, the top row represents polyhedral vertex labels, and the bottom row represents ligand labels.

For convenience, the non-identity operation (namely a or i) in the factor C / can be called a primary involution and designated as S'. Note that some point groups can have more than one primary involution. Thus the point group C2v has two different o vprimary involutions. Some point groups are direct products of the type R x C f in which both R and C f are normal subgroups. These are listed in Table 2-2. Because of the direct product structure, the primary involution in such a group is in a class by itself.

Sites permuted by a transitive permutation group are thus equivalent. Transitive permutation groups represent permutation groups of the “highest symmetry” and thus play a special role in permutation group theory. The maximum number of distinct permutations of n objects is n\. The corresponding group is called the symmetric group of degree n and is traditionally designated as Sn. However, this designation can easily be confused with the designation Sn used by chemists for an improper rotation, so that the alternative designation of Pn for the symmetric group on n objects causes less confusion in chemical contexts.

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