Fibonacci polynomials and parity domination in grid graphs
type: Item
instance of: scholarly article
title: Fibonacci polynomials and parity domination in grid graphs
zbMATH Open document ID: 0999.05079
author: John Goldwasser
author: Henry Ware
author: William F. Klostermeyer
published in: Graphs and Combinatorics
publication date: 2002-07-29T00:00:00Z
review text: Analogously to the sequence of Fibonacci numbers also the sequence of Fibonacci polynomials is defined. They are polynomials of one variable \(x\) over the field of real numbers or over some Galois field. In any case the sequence of Fibonacci polynomials \(f_0,f_1,f_2,\dots\) is defined recurrently so that \(f_0= 0\), \(f_1=1\), \(f_i= f_{i-1}+ xf_{i-2}\) for \(i\geq 2\). In the paper Fibonacci polynomials over the Galois field \(\text{GF}(2)\) are used to investigate even domination in grid graphs. An even dominating set in a graph \(G\) is a set \(S\) with the property that each vertex of \(G\) is adjacent to an even number of vertices of \(S\) (coinciding vertices are also considered as adjacent).
reviewed by: Bohdan Zelinka
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1773378
zbMATH Keywords: Fibonacci polynomial
zbMATH Keywords: finite field
zbMATH Keywords: grid graph
zbMATH Keywords: lights out
zbMATH Keywords: even dominating set
MaRDI profile type: Publication
full work available at URL: s003730200020
OpenAlex ID: W1978836719
DOI: 10.1007/S003730200020
description: scientific article; zbMATH DE number 1773378