ON DISCERNING SYMMETRY PROPERTIES OF GRAPHS
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Publisher:Ohio State University
A procedure which allows the symmetry properties of graphs to be systematically investigated is outlined. It consists in finding all distinctive labelings of the vertices of a graph of a prescribed form. In contrast to the usual situation of characterizing symmetry properties of molecules in the case of related graphs there is no prior knowledge of the relevant symmetry operations. The outlined scheme derives all symmetry operations (i.e., permutations of labels) which leave the connectivity of the graph invariant. As illustrations, it is shown that Petersen graph and Desaurges-Levy graph (both of interest in discussions: of trigonal bipyramidal rearrangements) belong to symmetry groups of order 120 and 240 respectively. The approach provides a basis for considerations of symmetry properties of non-rigid molecules.
Author Institution: Department of Chemistry, Tufts university
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