Signed Total Domination and Mycielski Structure in Graphs

2017 ◽  
pp. 102-106
Author(s):  
Arezoo. N. Ghameshlou ◽  
Athena Shaminezhad
Keyword(s):  
Total Domination ◽  
Signed Total Domination

Global signed total domination in graphs

2011 ◽  
Vol 79 (1-2) ◽  
pp. 7-22 ◽  
Author(s):  
MARYAM ATAPOUR ◽  
SEYED MAHMOUD SHEIKHOLESLAMI ◽  
ABDOLLAH KHODKAR
Keyword(s):  
Total Domination ◽  
Signed Total Domination ◽  
Domination In Graphs

COMPLEXITY OF CERTAIN FUNCTIONAL VARIANTS OF TOTAL DOMINATION IN CHORDAL BIPARTITE GRAPHS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250045 ◽  
Author(s):  
D. PRADHAN
Keyword(s):  
Dominating Set ◽  
Bipartite Graphs ◽  
Total Domination ◽  
Fixed Integer ◽  
Functional Variants ◽  
Total Dominating Set ◽  
Domination Problem ◽  
Signed Total Domination ◽  
The Cost ◽  
Chordal Bipartite Graphs

In this paper, we consider minimum total domination problem along with two of its variations namely, minimum signed total domination problem and minimum minus total domination problem for chordal bipartite graphs. In the minimum total domination problem, the objective is to find a smallest size subset TD ⊆ V of a given graph G = (V, E) such that |TD∩NG(v)| ≥ 1 for every v ∈ V. In the minimum signed (minus) total domination problem for a graph G = (V, E), it is required to find a function f : V → {-1, 1} ({-1, 0, 1}) such that f(NG(v)) = ∑u∈NG(v)f(u) ≥ 1 for each v ∈ V, and the cost f(V) = ∑v∈V f(v) is minimized. We first show that for a given chordal bipartite graph G = (V, E) with a weak elimination ordering, a minimum total dominating set can be computed in O(n + m) time, where n = |V| and m = |E|. This improves the complexity of the minimum total domination problem for chordal bipartite graphs from O(n2) time to O(n + m) time. We then adopt a unified approach to solve the minimum signed (minus) total domination problem for chordal bipartite graphs in O(n + m) time. The method is also able to solve the minimum k-tuple total domination problem for chordal bipartite graphs in O(n + m) time. For a fixed integer k ≥ 1 and a graph G = (V, E), the minimum k-tuple total domination problem is to find a smallest subset TDk ⊆ V such that |TDk ∩ NG(v)| ≥ k for every v ∈ V.

Signed total domination in nearly regular graphs

2006 ◽  
Vol 10 (1) ◽  
pp. 4-8 ◽  
Author(s):  
Li-ying Kang ◽  
Er-fang Shan
Keyword(s):  
Regular Graphs ◽  
Total Domination ◽  
Signed Total Domination

Signed Total Domination Nnumber of a Graph

2001 ◽  
Vol 51 (2) ◽  
pp. 225-229 ◽  
Author(s):  
Bohdan Zelinka
Keyword(s):  
Total Domination ◽  
Signed Total Domination

scholarly journals Remarks on the minus (signed) total domination in graphs

2008 ◽  
Vol 308 (15) ◽  
pp. 3373-3380 ◽  
Author(s):  
Erfang Shan ◽  
T.C.E. Cheng
Keyword(s):  
Total Domination ◽  
Signed Total Domination ◽  
Domination In Graphs

Bold signed total domination for complete multi-partite graph

2015 ◽  
Vol 9 ◽  
pp. 1627-1637
Author(s):  
K. R. Nithyakalyani ◽  
K. Subramanian
Keyword(s):  
Total Domination ◽  
Signed Total Domination
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