Combinatorial properties of graphs and groups of physico-chemical interest

Combinatorial properties of graphs and groups of physico-chemical interest are described. A type of mathematical modeling is applied which involves "translating" algebraic expressions into graphs. The idea is applied to both graph theory and group theory. The former topic includes objects of importance in physics and chemistry such as trees, polyomino graphs, king boards, etc. Our study along these lines emphasizes nonadjacency relations, graph-generation, quasicrystals, continued fractions, fractals, and general ordering schemes of graphs. The second part of the paper considers certain colored graphs as models of several group-theoretical concepts including coset representations of groups, subduction of groups, character tables, and mark tables which are essential to the understanding of recent developments of combinatorial enumeration in chemistry.