Please use this identifier to cite or link to this item:
Title: Parity of an odd dominating set
Authors: Batal, Ahmet
Keywords: Lights out
All-ones problem
Odd dominating set
Parity domination
Domination number
Issue Date: 2022
Abstract: For a simple graph $G$ with vertex set $V(G)={v_1,...,v_n}$, we define the closed neighborhood set of a vertex $u$ as $N[u]={v in V(G) ; | ; v ; text{is adjacent to} ; u ; text{or} ; v=u }$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$. We say a set $S$ is odd dominating if $N[u]cap S$ is odd for all $uin V(G)$. We prove that the parity of the cardinality of an odd dominating set of $G$ is equal to the parity of the rank of $G$, where rank of $G$ is defined as the dimension of the column space of $N(G)$. Using this result we prove several corollaries in one of which we obtain a general formula for the nullity of the join of graphs.
ISSN: 1303-5991
Appears in Collections:Mathematics / Matematik
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection

Files in This Item:
File SizeFormat 
document.pdf443.46 kBAdobe PDFView/Open
Show full item record

CORE Recommender

Page view(s)

checked on Feb 23, 2024


checked on Feb 23, 2024

Google ScholarTM



Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.