1 Journal of Integer Sequences, Vol 5 (2002), Article 02.1.6 Direct Enumeration of Chiral and Achiral Graphs of a Polyheterosubstituted Monocyclic Cycloalkane. Robert M. NEMBA, Alphonse EMADAK Faculty of Science, Laboratory of Theoretical Chemistry Section of Molecular Topology University of Yaounde I, P. O. Box 812 Yaounde, Cameroon Email addresses: rnemba@yahoo.fr, emadak@uycdc.uninet.cm Abstract A general pattern inventory is given for a direct enumeration of chiral and achiral graphs of any polyheterosubstituted monocyclic cycloalkane with an empirical formula k i m m m n Z Y X C ... .... 1 satisfying the condition . 2 ... ... 1 n m m m k i = + + + + (1) 1. INTRODUCTION The application of different enumeration tools to numerous problems of chemistry is an attractive point for mathematicians and chemists. The abundant chemistry literature on this subject deals with Plyas counting theorem[1,2] in the series of acyclic organic molecules and among the articles published in this field, one may retain the contribution of Balasubramanian[3,4] who has presented the generalized wreath product method for the enumeration of stereo and position isomers of polysubstituted organic compounds and later explored the applications of combinatorics and graph theory to spectroscopy and quantum chemistry. The idea to calculate the sequences of exact numbers of chiral and achiral skeletons for any molecule of the series of homopolysubstituted monocyclic cycloalkanes m m n n X H C - 2 , (X being a non isomerisable substituent), has been discussed by Nemba and Ngouhouo [5], Nemba[6], Nemba and Fah [7], Nemba and Balaban [8].