Maximal independent sets on a grid graph

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

An independent vertex set of a graph is a set of vertices of the graph in which no two vertices are adjacent, and a maximal independent set is one that is not a proper subset of any other independent set. In this paper we count the number of maximal independent sets of vertices on a complete rectangular grid graph. More precisely, we provide a recursive matrix-relation producing the partition function with respect to the number of vertices. The asymptotic behavior of the maximal hard square entropy constant is also provided. We adapt the state matrix recursion algorithm, recently invented by the author to answer various two-dimensional regular lattice model problems in enumerative combinatorics and statistical mechanics.

Original languageEnglish
Pages (from-to)2762-2768
Number of pages7
JournalDiscrete Mathematics
Volume340
Issue number12
DOIs
Publication statusPublished - 2017 Dec 1

Fingerprint

Grid Graph
Maximal Independent Set
Enumerative Combinatorics
Proper subset
Statistical mechanics
Graph in graph theory
Independent Set
Lattice Model
Statistical Mechanics
Recursion
Partition Function
Count
Entropy
Adjacent
Asymptotic Behavior
Vertex of a graph

Keywords

  • Enumeration
  • Grid graph
  • Maximal independent set

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Maximal independent sets on a grid graph. / Oh, Seung Sang.

In: Discrete Mathematics, Vol. 340, No. 12, 01.12.2017, p. 2762-2768.

Research output: Contribution to journalArticle

Oh, Seung Sang. / Maximal independent sets on a grid graph. In: Discrete Mathematics. 2017 ; Vol. 340, No. 12. pp. 2762-2768.
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