Applications of caterpillar trees in chemistry and physics

The relations of caterpillar trees (which are also known as Gutman trees and benzenoid trees) to other mathematical objects such as polyhex graphs, Clar graphs, king polyominos, rook boards and Young diagrams are discussed. Potential uses of such trees in data reduction, computational graph theory, and in the ordering of graphs are considered. Combinatorial and physical properties of benzenoid hydrocarbons can be studied via related caterpillars. It thus becomes possible to study the properties of large graphs such as benzenoid (i.e. polyhex) graphs in terms of much smaller tree graphs. Generation of the cyclic structures of wreath and generalized wreath product groups through the use of caterpillar trees is illustrated.