# Search results for: Nader Jafari Rad

Graphs and Combinatorics > 2019 > 35 > 3 > 599-609

*S*of vertices in a graph

*G*is an

*identifying code*if for every pair of vertices

*x*and

*y*of

*G*, the sets $$N[x]\cap S$$ N [ x ] ∩ S and $$N[y]\cap S$$ N [ y ] ∩ S are non-empty and different. The minimum cardinality of an identifying code...

Discussiones Mathematicae Graph Theory > 2017 > 38 > 1 > 49-62

Graphs and Combinatorics > 2018 > 34 > 1 > 193-205

*S*of

*V*is said to be an $$\alpha $$ α

*-dominating set*if for all $$v \in V {\setminus } S, |N(v)\cap S|\ge \alpha |N(v)|$$ v∈V\S,|N(v)∩S|≥α|N(v)| . The size of a smallest such

*S*is called the $$\alpha $$ α

*-domination number*and is denoted by $$\gamma _{\alpha }(G)$$ γα(G) ....

Discussiones Mathematicae Graph Theory > 2017 > 37 > 4 > 859-871

Graphs and Combinatorics > 2017 > 33 > 4 > 913-927

*S*of vertices in a graph

*G*is a 2-step dominating set of

*G*if every vertex is 2-step dominated by some vertex of

*S*. A subset

*S*of vertices of

*G*is a hop dominating set if every vertex outside

*S*is 2-step dominated by some vertex of

*S*. The hop domination number, $$\gamma _{h}(G)$$ γ h ( G...

Discrete Applied Mathematics > 2017 > 217 > P2 > 210-219

Discussiones Mathematicae Graph Theory > 2016 > 36 > 4 > 877-887

Discussiones Mathematicae Graph Theory > 2016 > 36 > 3 > 629-641

Discrete Mathematics > 2016 > 339 > 7 > 1909-1914

Graphs and Combinatorics > 2016 > 32 > 3 > 1155-1166

*S*of

*G*, we say that

*S*is an $$\alpha $$ α -dominating set if for any $$v\in V-S, |N(v)\cap S| \ge \alpha |N(v)|$$ v ∈ V - S , | N ( v ) ∩ S | ≥ α | N ( v ) | . The cardinality of a smallest $$\alpha...

Journal of Complexity > 2015 > 31 > 5 > 754-761

Proceedings - Mathematical Sciences > 2015 > 125 > 3 > 271-276

*G*=(

*V*,

*E*) be a graph without isolated vertices. A dominating set

*S*of

*G*is called a neighborhood total dominating set (or just NTDS) if the induced subgraph

*G*[

*N*(

*S*)] has no isolated vertex. The minimum cardinality of a NTDS of

*G*is called the neighborhood total domination number of

*G*and is denoted by

*γ*

_{nt}(

*G*). In this paper, we obtain sharp bounds for the neighborhood total domination number of a...

National Academy Science Letters > 2015 > 38 > 3 > 263-269

*G*is a set

*D*of vertices of

*G*such that every vertex of $$V(G) {\setminus} D$$ V ( G ) \ D has at least two neighbors in

*D*, and the set $$V(G) {\setminus} D$$ V ( G ) \ D is independent. The 2-outer-independent domination number of a graph

*G*is the minimum cardinality...

Graphs and Combinatorics > 2014 > 30 > 3 > 717-728

*b*

_{ t }(

*G*) of a graph

*G*with no isolated vertex is the cardinality of a smallest set of edges $${E^{\prime}\subseteq E(G)}$$ for which (1)

*G*−

*E*′ has no isolated vertex, and (2) $${\gamma_{t}(G-E^{\prime})>\gamma_{t}(G)}$$ . We improve some results on the total bondage number of a graph and give a constructive characterization of a certain class of trees achieving...

Discrete Applied Mathematics > 2013 > 161 > 18 > 3087-3089

Discrete Applied Mathematics > 2013 > 161 > 16-17 > 2460-2466

Discussiones Mathematicae Graph Theory > 2013 > 33 > 2 > 337-346

Graphs and Combinatorics > 2013 > 29 > 3 > 527-533

*G*is a function

*f*:

*V*(

*G*) → {0, 1, 2} satisfying the condition that every vertex

*u*for which

*f*(

*u*) = 0 is adjacent to at least one vertex

*v*for which

*f*(

*v*) = 2. The weight of a Roman dominating function is the value $${f(V(G))=\sum_{u \in V(G)}f(u)}$$ . The Roman domination number,

*γ*

_{ R }(

*G*), of

*G*is the minimum weight of a...

Graphs and Combinatorics > 2013 > 29 > 4 > 1125-1133

*rainbow domination function*of a graph

*G*is a function

*f*that assigns to each vertex a set of colors chosen from the set {1, 2}, such that for any $${v\in V(G), f(v)=\emptyset}$$ implies $${\bigcup_{u\in N(v)}f(u)=\{1,2\}.}$$ The 2-

*rainbow domination number γ*

_{ r2}(

*G*) of a graph

*G*is the minimum $${w(f)=\Sigma_{v\in V}|f(v)|}$$ over all such functions

*f*. Let

*G*be a connected graph...

Acta Mathematica Sinica, English Series > 2013 > 29 > 6 > 1033-1042

*S*of vertices of a graph

*G*with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in

*S*and every vertex in

*V*(

*G*) −

*S*is also adjacent to a vertex in

*V*(

*G*) −

*S*. The total restrained domination number of

*G*is the minimum cardinality of a total restrained dominating set of

*G*. In this paper we initiate the study of total restrained bondage in graphs...