Mathematical Chemistry: (3,g)-Cages with Girth g, Topological Indices, and Other Graph-Theoretical Problems

Issue title: Contagious Creativity – In Honor of the 80th Birthday of Professor Solomon Marcus

Article type: Research Article

Authors: Balaban, Alexandru T.

Affiliations: Texas A&M University at Galveston, Marine Sciences Department, Galveston, TX, USA. balabana@tamug.edu

Note: [] Address for correspondence: Texas A&M University at Galveston, Marine Sciences Department, Galveston, TX, USA

Abstract: This essay contains personal views about mathematical chemistry — mainly with nonnumerical and non-quantumflavor. Similarities between mathematics and chemistry are pointed out, mainly based on the invention aspect of these two sciences, in contrast to discoveries characterizing most natural sciences. The author's involvement with chemical applications of graph theory needed a biographical background. Then five topics are reviewed: (1) enumerations of certain classes of chemical compounds initiated in collaboration with Professors Silviu Teleman and Frank Harary; (2) the (3,g)-cages with g=10 and 11; (3) isoprenoid structures modeled in collaboration with Professor Solomon Marcus by cellular automata and picture grammars; (4) benzenoid polycyclic hydrocarbons described in collaboration with Professor Ioan Tomescu; and (5) topological indices.

Keywords: Graph theory, g-cages, isoprenoid structures, topological index

Journal: Fundamenta Informaticae, vol. 64, no. 1-4, pp. 1-16, 2005