### 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.

Original language | English |
---|---|

Pages (from-to) | 192-204 |

Number of pages | 13 |

Journal | Linear Algebra and Its Applications |

Volume | 510 |

DOIs | |

Publication status | Published - 2016 Dec 1 |

### Fingerprint

### Keywords

- Enumeration
- Hard square
- Independent vertex set
- Merrifield–Simmons index

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

### Cite this

*Linear Algebra and Its Applications*,

*510*, 192-204. https://doi.org/10.1016/j.laa.2016.08.025

**Enumerating independent vertex sets in grid graphs.** / Oh, Seung Sang; Lee, Sangyop.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 510, pp. 192-204. https://doi.org/10.1016/j.laa.2016.08.025

}

TY - JOUR

T1 - Enumerating independent vertex sets in grid graphs

AU - Oh, Seung Sang

AU - Lee, Sangyop

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - Enumeration

KW - Hard square

KW - Independent vertex set

KW - Merrifield–Simmons index

UR - http://www.scopus.com/inward/record.url?scp=84983567710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983567710&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2016.08.025

DO - 10.1016/j.laa.2016.08.025

M3 - Article

VL - 510

SP - 192

EP - 204

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -