Some Applications of Caterpillar (Gutman = Benzenoid) Trees in Chemistry and Physics.

Abstract

Relations of caterpillar trees (also called 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. Thus it is possible to study the properties of large graphs such as benzenoid (= 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. Keywords: Graph theory, Caterpillar trees, Gutman trees, Rook boards, Clar graphs, Young diagrams, Wreath product groups.

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Document Details

Document Type
Technical Report
Publication Date
Aug 11, 1987
Accession Number
ADA183889

Entities

People

  • Sherif El-basil

Organizations

  • University of Georgia

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Absorption Spectra
  • Cells
  • Chemistry
  • Computational Science
  • Computations
  • Data Reduction
  • Electrons
  • Elements
  • Graph Theory
  • Hydrocarbons
  • Lepidoptera
  • Organic Chemistry
  • Permutations
  • Physical Properties
  • Physics
  • Polynomials
  • Sequences

Readers

  • Graph Algorithms and Convex Optimization.