• Home
  • Browse
    • Current Issue
    • By Issue
    • By Author
    • By Subject
    • Author Index
    • Keyword Index
  • Journal Info
    • About Journal
    • Aims and Scope
    • Editorial Board
    • Advisory Board
    • Editorial Staff
    • Publication Ethics
    • Indexing and Abstracting
    • Related Links
    • FAQ
    • Peer Review Process
    • News
  • Guide for Authors
  • Submit Manuscript
  • Reviewers
  • Contact Us
 
  • Login
  • Register
Home Articles List Article Information
  • Save Records
  • |
  • Printable Version
  • |
  • Recommend
  • |
  • How to cite Export to
    RIS EndNote BibTeX APA MLA Harvard Vancouver
  • |
  • Share Share
    CiteULike Mendeley Facebook Google LinkedIn Twitter Telegram
Transactions on Combinatorics
Articles in Press
Current Issue
Journal Archive
Volume Volume 7 (2018)
Volume Volume 6 (2017)
Volume Volume 5 (2016)
Volume Volume 4 (2015)
Volume Volume 3 (2014)
Volume Volume 2 (2013)
Volume Volume 1 (2012)
Issue Issue 4
Issue Issue 3
Issue Issue 2
Issue Issue 1
P. Kazemi, A. (2012). $k$-Tuple total domination and mycieleskian graphs. Transactions on Combinatorics, 1(1), 7-13. doi: 10.22108/toc.2012.333
Adel P. Kazemi. "$k$-Tuple total domination and mycieleskian graphs". Transactions on Combinatorics, 1, 1, 2012, 7-13. doi: 10.22108/toc.2012.333
P. Kazemi, A. (2012). '$k$-Tuple total domination and mycieleskian graphs', Transactions on Combinatorics, 1(1), pp. 7-13. doi: 10.22108/toc.2012.333
P. Kazemi, A. $k$-Tuple total domination and mycieleskian graphs. Transactions on Combinatorics, 2012; 1(1): 7-13. doi: 10.22108/toc.2012.333

$k$-Tuple total domination and mycieleskian graphs

Article 2, Volume 1, Issue 1, March 2012, Page 7-13  XML PDF (415 K)
Document Type: Research Paper
DOI: 10.22108/toc.2012.333
Author
Adel P. Kazemi
UMA (University of Mohaghegh Ardabili)
Abstract
‎Let $k$ be a positive integer‎. ‎A subset $S$ of $V(G)$ in a graph $G$‎ ‎is a $k$-tuple total dominating set of $G$ if every vertex of $G$‎ ‎has at least $k$ neighbors in $S$‎. ‎The $k$-tuple total domination‎ ‎number $\gamma _{\times k,t}(G)$ of $G$ is the minimum cardinality‎ ‎of a $k$-tuple total dominating set of $G$‎. ‎In this paper for a‎ ‎given graph $G$ with minimum degree at least $k$‎, ‎we find some sharp‎ ‎lower and upper bounds on the $k$-tuple total domination number of the $m$‎ -‎Mycieleskian graph $\mu _{m}(G)$ of $G$ in terms on $k$ and $\gamma‎ ‎_{\times k,t}(G)$‎. ‎Specially we give the sharp bounds $\gamma‎ ‎_{\times k,t}(G)+1$ and $\gamma _{\times k,t}(G)+k$ for $\gamma‎ ‎_{\times k,t}(\mu _1(G))$‎, ‎and characterize graphs with $\gamma‎ ‎_{\times k,t}(\mu _1(G))=\gamma _{\times k,t}(G)+1$‎.
Keywords
$k$-tuple total dominating set; k-tuple total domination number; $m$-Mycieleskian graph
Main Subjects
05C69 Dominating sets, independent sets, cliques
References
F. Harary, T. W. Haynes (2000). Double domination in graphs. Ars Combin.. 55, 201-213
T. W. Haynes, S. T. Hedetniemi and P. J. Slater (1998). Fundamentals of Domination in Graphs. Marcel Dekker, New York.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater (1998). Domination in Graphs: Advanced Topics. Marcel Dekker, New York.
M. A. Henning, A. P. Kazemi (2010). k-tuple total domination in graphs. Discrete Applied Mathematics. 158, 1006-1011
M. A. Henning, A. P. Kazemi k-tuple total domination in cross product graphs. Journal of Combinatorial Optimization.
A. P. Kazemi k-tuple total domination in complementary prisms. ISRN Discrete Mathematics.
C. Tardif (2001). Fractional chromatic numbers of cones over graphs. J. Graph Theory. 38, 87-94
D. B. West (2001). Introduction to Graph Theory, (2nd edition). Prentice Hall, USA.
Statistics
Article View: 4,573
PDF Download: 3,615
Home | Glossary | News | Aims and Scope | Sitemap
Top Top

Journal Management System. Designed by sinaweb.