An Improved Upper Bound on the Total Restrained Domination Number in Cubic Graphs

2011 ◽  
Vol 28 (4) ◽  
pp. 547-554 ◽  
Author(s):  
Justin Southey ◽  
Michael A. Henning
Keyword(s):  
Upper Bound ◽  
Domination Number ◽  
Cubic Graphs ◽  
Restrained Domination ◽  
Total Restrained Domination ◽  
Total Restrained Domination Number ◽  
Restrained Domination Number

scholarly journals -Tuple Total Restrained Domination in Complementary Prisms

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Adel P. Kazemi
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Restrained Domination ◽  
Minimum Number ◽  
Total Restrained Domination ◽  
Complementary Prism ◽  
Total Restrained Domination Number ◽  
Restrained Domination Number

In a graph with , a -tuple total restrained dominating set is a subset of such that each vertex of   is adjacent to at least vertices of and also each vertex of is adjacent to at least vertices of  . The minimum number of vertices of such sets in is the -tuple total restrained domination number of . In [-tuple total restrained domination/domatic in graphs, BIMS], the author initiated the study of the -tuple total restrained domination number in graphs. In this paper, we continue it in the complementary prism of a graph.

scholarly journals An upper bound on the domination number of n-vertex connected cubic graphs

2009 ◽  
Vol 309 (5) ◽  
pp. 1142-1162 ◽  
Author(s):  
A.V. Kostochka ◽  
B.Y. Stodolsky
Keyword(s):  
Upper Bound ◽  
Domination Number ◽  
Cubic Graphs
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