domination number
Comparison of Roman Domination Number with Domination Number, Independent Domination Number and Chromatic Number of a Graph
... The number of edges incident with a vertex v of a graph is called the degree of v and is denoted by ...The domination number (G) of the graph G is the minimum cardinality of the dominating set in ...
7
Triple Domination Number of a Butterfly Graph
... By the symmetric structure of BF(n), the domination number must be even. Therefore │S│ is even. Suppose │ S│= 14. Then by symmetry 7 vertices in the left copy and 7 vertices in the right copy are selected. ...
5
Split and Non–Split Domination Number in Bipolar Fuzzy Graphs
... Definition 2.14. A subset V of is called a dominating set in if for every ∈ – V, there exist K ∈ V such that K dominates . A dominating set V of a BFG is said to be minimal dominating set if no proper subset of V is a ...
7
The Ratio of the Irredundance Number and the Domination Number for Block Cactus Graphs
... Let γ (G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [1] and Bollob´ as and Cockayne [2] proved independently that γ(G) < 2 ...
10
Forcing Independent Domination Number of a Graph
... and domination concepts in 1997 and used the term "forcing domination ...Independent domination under some binary operations such as corona and composition is studied by Canoy ...independence ...
11
A Review on Lower Bounds for the Domination Number
... independence number is at least the radius – originally a conjecture of Graffiti and proven independently several ...total domination number (that is, the cardinality of a set of minimum order having ...
5
About m-domination number of graphs
... m-domination number which is the minimum cardinality of an m-dominating ...m-domination number increases or decreases when a vertex is removed from the ...
5
Vertex Domination Number in S-valued Graphs
... vertex domination numbers have been obtained by several authors ([5 ], [9], ...vertex domination number for S-valued ...vertex domination number will be a generalization of the bounds ...
6
The Split Majority Domination Number of a Graph
... Definition 2.1. A majority dominating set D ⊆ V(G) is said to be split majority dominating set if the induced sub graph < V – D > is disconnected. A split majority dominating set D is minimal if no proper subset of ...
10
The Disjoint Total Domination Number of a Graph
... the closed neighborhood of S is N[S] = N(S) ∪ S. A set D ⊆ V is a dominating set if every vertex in V – D adjacent to a vertex in D, that is N[D] = V. The domination number γ(G) of G is the minimum ...
6
On the k-Metro Domination Number of Paths
... Metro domination number introduced by Sooryanarayana and Raghunath [5]. Fink and Jacobson [6, 7] in 1985 introduced the concept of multiple domination. A subset D of V (G) is k-dominating in G if ...
8
The k tuple domination number revisited
... and maximum degrees of vertices of G, respectively. Put δ = δ(G) and ∆ = ∆(G). A set X is called a dominating set if every vertex not in X is adjacent to a vertex in X. The minimum cardinality of a dominating set of G is ...
7
Complementary Perfect Domination Number of Regular Graphs
... describe domination number of regular graphs as well as complimentary perfect domination number and induced complimentary perfect domination number, denoted by cpd and ...
5
On The K- Metro Domination Number of Cycle
... k-metro domination number of a cycle is the order of a smallest k-dominating set of which resolves as a metric ...k-metro domination number of ...
6
Edge Roman Star Domination Number on Graphs
... Roman domination called edge Roman star ...star domination number of star graphs, paths, cycles, complete binary trees and Petersen ...edge domination number are presented for general ...
10
On strong domination number of corona related graphs
... strong domination number. The relation between strong domination and maximum degree of the graph as well as weak domination and minimum degree of the graph were revealed by Swaminathan and ...
5
ON THE AVERAGE LOWER 2-DOMINATION NUMBER OF A GRAPH
... The aim of this paper is to define a new vulnerability parameter, so called average lower 2-domination number. In the Section 2, well-known basic results have been given for the average lower ...
8
The Forcing Monophonic Hull Domination Number of a Graph
... Proof. For the complete graph , it follows from Theorem that the set of all vertices of is the unique monophonic hull dominating set of . Hence it follows from Theorem 2.5(a) that . For any non-trivial tree , the ...
9
The Upper Total Edge Domination Number of a Graph
... The total edge dominating set in a connected graph is called a minimal total edge dominating set if no proper subset of is a total edge dominating set of . The upper total edge domination number ( ) of is ...
6
On The Upper Open Geodetic Domination Number of a Graph
... geodetic domination number of and is denoted by ( ...geodetic domination set of is the upper open geodetic domination number of and is denoted by ( ...dominating number of ...
11