Caterpillar (Gutman) trees in chemical graph theory
Gutman trees (also known as caterpillar trees and benzenoid trees) are demonstrated to be elegant storage devices of information on graph-theoretical properties of many mathematical objects including benzenoid graphs, rook boards, king polyomino graphs, Clar graphs, and Young diagrams. The notion of a “restricted” equivalence relation is considered to relate these graphs. The uses of caterpillars in various areas of physico-chemical interests such as modeling of interactions, computational chemistry and ordering of graphs are discussed. Namely, caterpillar trees are used to model wreath product groups, Clar structures and nonadjacency relations in graphs of chemical interest. Further, they are used to study several properties of benzenoid hydrocarbons including UV absorption spectrum, molecular susceptibility, anisotropy, heat of atomization as well as Diels-Alder addition rate constant. Several novel relations correlating the connectivity of a caterpillar tree with several combinatorial properties of benzenoid hydrocarbons, such as, Kekulé counts, conjugated circuits, Sachs graphs, and self-avoiding paths, are presented.
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