k-Tuple Total Domination in Complementary Prisms
Author
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-01-18
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Let k be a positive integer, and let G be a graph with minimum degree at least k.
In their study (2010), Henning and Kazemi defined the k-tuple total domination number γ×k,tG of G as the minimum cardinality of a k-tuple total dominating set of G, which is a vertex set such that every vertex of G is adjacent to at least k vertices in it.
If G̅ is the complement of G, the complementary prism GG̅ of G is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅.
In this paper, we extend some of the results of Haynes et al.
(2009) for the k-tuple total domination number and also obtain some other new results.
Also we find the k-tuple total domination number of the complementary prism of a cycle, a path, or a complete multipartite graph.
American Psychological Association (APA)
Kazemi, Adel P.. 2012. k-Tuple Total Domination in Complementary Prisms. ISRN Discrete Mathematics،Vol. 2011, no. 2011, pp.1-13.
https://search.emarefa.net/detail/BIM-490046
Modern Language Association (MLA)
Kazemi, Adel P.. k-Tuple Total Domination in Complementary Prisms. ISRN Discrete Mathematics No. 2011 (2011), pp.1-13.
https://search.emarefa.net/detail/BIM-490046
American Medical Association (AMA)
Kazemi, Adel P.. k-Tuple Total Domination in Complementary Prisms. ISRN Discrete Mathematics. 2012. Vol. 2011, no. 2011, pp.1-13.
https://search.emarefa.net/detail/BIM-490046
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-490046