### 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 |
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Pages (from-to) | 192-204 |

Number of pages | 13 |

Journal | Linear Algebra and Its Applications |

Volume | 510 |

DOIs | |

Publication status | Published - 2016 Dec 1 |

### 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

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## Cite this

Oh, S. S., & Lee, S. (2016). Enumerating independent vertex sets in grid graphs.

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