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Enumerating independent vertex sets in grid graphs
- Authors
- Oh, Seungsang; Lee, Sangyop
- Issue Date
- 1-12월-2016
- Publisher
- ELSEVIER SCIENCE INC
- Keywords
- Independent vertex set; Merrifield-Simmons index; Hard square; Enumeration
- Citation
- LINEAR ALGEBRA AND ITS APPLICATIONS, v.510, pp.192 - 204
- Indexed
- SCIE
SCOPUS
- Journal Title
- LINEAR ALGEBRA AND ITS APPLICATIONS
- Volume
- 510
- Start Page
- 192
- End Page
- 204
- ISSN
- 0024-3795
- Abstract
- A set of vertices in a graph is called independent if no two vertices of the set are connected by an edge. In this paper we use the state matrix recursion algorithm, developed by Oh, to enumerate independent vertex sets in a grid graph and even further to provide the generating function with respect to the number of vertices. We also enumerate bipartite independent vertex sets in a grid graph. The asymptotic behavior of their growth rates is presented. (C) 2016 Elsevier Inc. All rights reserved.
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