Enumerating independent vertex sets in grid graphs

Seung Sang Oh, Sangyop Lee

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)192-204
Number of pages13
JournalLinear Algebra and Its Applications
Volume510
DOIs
Publication statusPublished - 2016 Dec 1

Fingerprint

Grid Graph
Vertex of a graph
Recursion
Generating Function
Asymptotic Behavior
Graph in graph theory

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

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

In: Linear Algebra and Its Applications, Vol. 510, 01.12.2016, p. 192-204.

Research output: Contribution to journalArticle

@article{7bc4f29ab55a437d8e021d444b528f86,
title = "Enumerating independent vertex sets in grid graphs",
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.",
keywords = "Enumeration, Hard square, Independent vertex set, Merrifield–Simmons index",
author = "Oh, {Seung Sang} and Sangyop Lee",
year = "2016",
month = "12",
day = "1",
doi = "10.1016/j.laa.2016.08.025",
language = "English",
volume = "510",
pages = "192--204",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",

}

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 -