Extremal Polygonal Chains Concerning Merrified-Simmons Index. (1st January 2017)

• Record Type: Journal Article
• Authors: Cao, Yuefen; Yang, Weiling; Zhang, Fuji
• Is Part Of: Polycyclic aromatic compounds. Volume 37:Number 1(2017)
• Page Start: 1
• Page End: 23
• Publication Date: 2017-01-01
• Subjects: k-independent set -- polygonal chain -- Y-polynomial; Polycyclic aromatic compounds -- Periodicals; 547
• DOI: 10.1080/10406638.2015.1066405
• Languages: English
• ISSNs: 1040-6638

Abstract

ABSTRACT: Denote by the set of h -polygonal chains with n congruent regular h -polygons ( h ⩾ 6). For any, let ik ( An ) be the numbers of k -independent sets of An . In this article, we show that ik ( Z 2 n ) ⩾ ik ( An ) ⩾ ik ( Z 1 n ) for any k ⩾ 0, with the equalities on the left holding for all k only if An = Z 2 n, and the equalities on the right holding for all k only if An = Z 1 n, where Z 1 n and Z 2 n are extremal chains of type one and type two (their definitions are given in the main text), respectively. Thus, we extend the main results of (7 ) to a more general case.