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 language English 192-204 13 Linear Algebra and Its Applications 510 https://doi.org/10.1016/j.laa.2016.08.025 Published - 2016 Dec 1

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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

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

Research output: Contribution to journalArticle

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