Secure Super Domination in Graphs

2021 ◽  
Vol 67 (8) ◽  
pp. 38-44
Author(s):  
Hemeh Luck M. Maravillas ◽  
Enrico L. Enriquez
Keyword(s):  
Domination In Graphs

Generalization of the total outer-connected domination in graphs

2016 ◽  
Vol 50 (2) ◽  
pp. 233-239
Author(s):  
Nader Jafari Rad ◽  
Lutz Volkmann
Keyword(s):  
Domination In Graphs

Equitable Cototal Domination in Graphs

2012 ◽  
Vol 3 (7) ◽  
pp. 301-305
Author(s):  
Dr. B. Basavanagoud Dr. B. Basavanagoud ◽  
◽  
Vijay V Teli
Keyword(s):  
Domination In Graphs

Total Complementary Acyclic Domination in Graphs

2013 ◽  
Vol 3 (2) ◽  
pp. 5
Author(s):  
M. Valliammal ◽  
S. P. Subbiah ◽  
V. Swaminathan
Keyword(s):  
Domination In Graphs

Efficient Secure Domination in Graphs

2015 ◽  
Vol 5 (2) ◽  
pp. 59 ◽  
Author(s):  
P. Roushini Leely Pushpam ◽  
Suseendran Chitra
Keyword(s):  
Domination In Graphs ◽  
Secure Domination

SUPER EQUITABLE DOMINATION IN GRAPHS

2020 ◽  
Vol 9 (7) ◽  
pp. 4923-4928
Author(s):  
P. Nataraj ◽  
A. Wilson Baskar ◽  
V. Swaminathan
Keyword(s):  
Domination In Graphs

scholarly journals The algorithmic complexity of mixed domination in graphs

2011 ◽  
Vol 412 (22) ◽  
pp. 2387-2392 ◽  
Author(s):  
Yancai Zhao ◽  
Liying Kang ◽  
Moo Young Sohn
Keyword(s):  
Algorithmic Complexity ◽  
Domination In Graphs

scholarly journals From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1036
Author(s):  
Abel Cabrera Martínez ◽  
Alejandro Estrada-Moreno ◽  
Juan Alberto Rodríguez-Velázquez
Keyword(s):  
Vertex Cover ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Special Issue ◽  
Total Domination Number ◽  
Theoretical Computer ◽  
Graph Parameters ◽  
Semitotal Domination ◽  
Domination In Graphs

This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x∈V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X⊆V(G) is defined to be N(X)=⋃x∈XN(x), while the external neighbourhood of X is defined to be Ne(X)=N(X)∖X. Now, for every set X⊆V(G) and every vertex x∈X, the external private neighbourhood of x with respect to X is defined as the set Pe(x,X)={y∈V(G)∖X:N(y)∩X={x}}. Let Xw={x∈X:Pe(x,X)≠⌀}. The strong differential of X is defined to be ∂s(X)=|Ne(X)|−|Xw|, while the quasi-total strong differential of G is defined to be ∂s*(G)=max{∂s(X):X⊆V(G)andXw⊆N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.

scholarly journals Inverse Equality Co-Neighborhood Domination in Graphs

2021 ◽  
Vol 1879 (3) ◽  
pp. 032036
Author(s):  
Sahib SH. Kahat ◽  
Manal N. Al-Harere
Keyword(s):  
Domination In Graphs
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