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Recognition of essentially disconnected benzenoids

Recognition of essentially disconnected benzenoids Vol.8 No.4 ACTA MATHEMATICAE APPLICATAE SINICA Oct., 1992 Study Bulletin RECOGNITION OF ESSENTIALLY DISCONNECTED BENZENOIDS" CHS RoNos, (S ( ColteCe o! Fi, lm,,~e =,ul E,:o,~,-,~8, F,u~&ou U.i,,ereitU, Fu.,bou SSO00~, Chi, m) S.J. CYVlN and B.N. CYVIN (The U,,~,,er~v of ~n~i~ Noway) 1. Introduction and Definitions A benzenoid, or a benzenoid system, is a connected planar graph whose every interior face is a regular hexagon. A peak (resp. valley) of a benzenoid is a vertex which lies above (reap. below) all its first neighbors. A Kekul4an benzenoid is a benzenoid with at least one perfect matching. An essentially disconnected benzenoid is a Kekul4an benzenoid which has some fixed bonds[I]. Essentially disconnected benzenoids have proved to be very useful in certain enumeration techniques for perfect matching[ 2[. Hence the problem of recognizing essentially disconnected benzenoids has attracted many researchers and several scientific papers have appeared{ 3-9]. In the search for criteria of essentially disconnected benzenoicls, the concept of horizontal g-cut plays an important role. A horizontal g-cut is either a horizontal cut or a horizontal proper g-cut; both of them are defined as follows[6]: Definition 1[ 5] . A collection of edges C is called a horizontal cut of a benzenoid http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Recognition of essentially disconnected benzenoids

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Publisher
Springer Journals
Copyright
Copyright © 1992 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006746
Publisher site
See Article on Publisher Site

Abstract

Vol.8 No.4 ACTA MATHEMATICAE APPLICATAE SINICA Oct., 1992 Study Bulletin RECOGNITION OF ESSENTIALLY DISCONNECTED BENZENOIDS" CHS RoNos, (S ( ColteCe o! Fi, lm,,~e =,ul E,:o,~,-,~8, F,u~&ou U.i,,ereitU, Fu.,bou SSO00~, Chi, m) S.J. CYVlN and B.N. CYVIN (The U,,~,,er~v of ~n~i~ Noway) 1. Introduction and Definitions A benzenoid, or a benzenoid system, is a connected planar graph whose every interior face is a regular hexagon. A peak (resp. valley) of a benzenoid is a vertex which lies above (reap. below) all its first neighbors. A Kekul4an benzenoid is a benzenoid with at least one perfect matching. An essentially disconnected benzenoid is a Kekul4an benzenoid which has some fixed bonds[I]. Essentially disconnected benzenoids have proved to be very useful in certain enumeration techniques for perfect matching[ 2[. Hence the problem of recognizing essentially disconnected benzenoids has attracted many researchers and several scientific papers have appeared{ 3-9]. In the search for criteria of essentially disconnected benzenoicls, the concept of horizontal g-cut plays an important role. A horizontal g-cut is either a horizontal cut or a horizontal proper g-cut; both of them are defined as follows[6]: Definition 1[ 5] . A collection of edges C is called a horizontal cut of a benzenoid

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References