Signed Domination Number of Some Graphs

2021 ◽  
Author(s):  
Saeid Alikhani ◽  
Fatemeh Ramezani
Keyword(s):  
Domination Number ◽  
Signed Domination ◽  
Signed Domination Number

Signed domination number of hypercubes

2021 ◽  
Author(s):  
B. ShekinahHenry ◽  
Y. S. Irine Sheela
Keyword(s):  
Domination Number ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Signed Domination ◽  
Vertex Set ◽  
Number Formula ◽  
Signed Domination Number

The [Formula: see text]-cube graph or hypercube [Formula: see text] is the graph whose vertex set is the set of all [Formula: see text]-dimensional Boolean vectors, two vertices being joined if and only if they differ in exactly one co-ordinate. The purpose of the paper is to investigate the signed domination number of this hypercube graphs. In this paper, signed domination number [Formula: see text]-cube graph for odd [Formula: see text] is found and the lower and upper bounds of hypercube for even [Formula: see text] are found.

Negative Signed Domination in Digraphs

2011 ◽  
Vol 65 ◽  
pp. 145-147
Author(s):  
Wen Sheng Li
Keyword(s):  
Directed Graph ◽  
Hamiltonian Cycle ◽  
Domination Number ◽  
Directed Cycle ◽  
Signed Domination ◽  
Signed Domination Number

The Concept of Negative Signed Domination Number of a Directed Graph Is Introduced. Exact Values Are Found for the Directed Cycle and Particular Types of Tournaments. Furthermore, it Is Proved that the Negative Signed Domination Number May Be Arbitrarily Big for Digraphs with a Directed Hamiltonian Cycle.

scholarly journals Upper signed domination number

2008 ◽  
Vol 308 (15) ◽  
pp. 3416-3419 ◽  
Author(s):  
Huajun Tang ◽  
Yaojun Chen
Keyword(s):  
Domination Number ◽  
Signed Domination ◽  
Signed Domination Number

LOWER BOUNDS OF SIGNED DOMINATION NUMBER OF A GRAPH

2004 ◽  
Vol 41 (1) ◽  
pp. 181-188 ◽  
Author(s):  
Moo-Young Sohn ◽  
Ja-Eun Lee ◽  
Soo-Young Kwon
Keyword(s):  
Lower Bounds ◽  
Domination Number ◽  
Signed Domination ◽  
Signed Domination Number

Signed domination and Mycielski’s structure in graphs

2020 ◽  
Vol 54 (4) ◽  
pp. 1077-1086
Author(s):  
Arezoo N. Ghameshlou ◽  
Athena Shaminezhad ◽  
Ebrahim Vatandoost ◽  
Abdollah Khodkar
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Minimum Weight ◽  
Domination Number ◽  
Upper Bounds ◽  
Underlying Graph ◽  
Signed Domination ◽  
Signed Domination Number ◽  
Dominating Function ◽  
Domination Numbers

Let G = (V, E) be a graph. The function f : V(G) → {−1, 1} is a signed dominating function if for every vertex v ∈ V(G), ∑x∈NG[v] f(x)≥1. The value of ω(f) = ∑x∈V(G) f(x) is called the weight of f. The signed domination number of G is the minimum weight of a signed dominating function of G. In this paper, we initiate the study of the signed domination numbers of Mycielski graphs and find some upper bounds for this parameter. We also calculate the signed domination number of the Mycielski graph when the underlying graph is a star, a wheel, a fan, a Dutch windmill, a cycle, a path or a complete bipartite graph.

scholarly journals On the signed domination number of some Cayley graphs

2020 ◽  
Vol 48 (7) ◽  
pp. 2825-2832
Author(s):  
Saeid Alikhani ◽  
Fatemeh Ramezani ◽  
Ebrahim Vatandoost
Keyword(s):  
Cayley Graphs ◽  
Domination Number ◽  
Signed Domination ◽  
Signed Domination Number
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