DOI: 10.1007/s10910-005-5423-7 Journal of Mathematical Chemistry Vol. 38, No. 2, August 2005 (© 2005) On the ordering of benzenoid chains and cyclo-polyphenacenes with respect to their numbers of Clar aromatic sextets Lusheng Wang Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong Fuji Zhang ∗ Department of Mathematics, Xiamen University, Xiamen Fujian, 361005 P.R.China E-mail: fjzhang@jingxian.xmu.edu.cn Hao Zhao Department of Computer Science, City Univeristy of Hong Kong, Kowloon, Hong Kong Received 15 December 2004; revised 24 January 2005 Based on Clar aromatic sextet theory [Clar, The Aromatic Serxtet (Wiley, New York, 1972)] and the concept of sextet polynomial introduced by Hosoya and Yamaguchi [Mathematical Concepts in Organic Chemistry (Springer, Berlin, 1986)], we define a new ordering of benzenoid systems. For two isomeric benzenoid systems B 1 and B 2 , we say B 1 >B 2 if each coefficient of sextet polynomial of B 1 is no less than the correspond- ing coefficient of sextet polynomial of B 2 . In this paper, we consider the ordering of the benzenoid chains. The maximal and second maximal benzenoid chains as well as the minimal, the second minimal up to the fourth minimal benzenoid chains are deter- mined. Furthermore, under this ordering, we determine the maximal and second max- imal cyclo-polyphenacenes as well as the minimal, the second minimal, and up to the seventh minimal cyclo-polyphenacenes. 1. Introduction Since many benzenoid hydrocarbons have been found from the high-temperature carbonization coal tar, these plane compounds with condensed benzene rings have been extensively studied in the last centenary. After the first monograph of Clar [1], several books and papers were published (see [2–6] and the references cited therein). The simplest benzenoid hydrocarbons are benzenoid chains (polyphenacenes). Up to now, many benzenoid chains have been prepared [1,7] and many theoretical and computational work has been done [8–10]. ∗ Corresponding address. 293 0259-9791/05/0800-0293/0 © 2005 Springer Science+Business Media, Inc.