Let G be a nontrivial connected graph. A dominating set D⊆ VG is called a doubly
connected dominating set of G if both D⟩ and VG\D⟩ are connected. Let D be a minimum …

Let 𝐺𝐺 be a graph. A dominating set 𝐷𝐷⊆ 𝑉𝑉 (𝐺𝐺) is called a secure dominating set of 𝐺𝐺
if for each vertex 𝑢𝑢∈ 𝑉𝑉 (𝐺𝐺)∖ 𝐷𝐷, there exists a vertex 𝑣𝑣∈ 𝐷𝐷 such that 𝑢𝑢𝑣𝑣∈ 𝐸𝐸 …

Let G be a connected simple graph. A dominating subset S of V (G) is a fair dominating set of
G if all the vertices not in S are dominated by the same number of vertices from S. Let D be a …

Let G be a connected simple graph and D be a minimum dominating set of G. A dominating
set S⊆ VG∖ D is called an inverse dominating set of G with respect to D. An inverse …

Let G bea connected simple graph. A dominating set S⊆ VG is called a perfect dominating
set of G if every u∈ VG\Sis dominated by exactly one element of S. Let D be a minimum …

In this paper, we initiate the study of super fair dominating set of a graph 𝐺 by giving the
super fair domination number of some special graphs. Further, we shows that given positive …

Let be a connected simple graph. A convex dominating set of is a convex secure dominating
set, if for each element thereexists an element such that and is adominating set. The convex …

Let G be a connected simple graph. A set S⊆ V (G) is a doubly connected dominating set if it
is dominating and both〈 S〉 and〈 V (G)∖ S〉 are connected. A nonempty subset S of the …

Let G=(V (G), E (G)) be a connnected simple graph. A subset S of V (G) is a dominating set of
G if for every u ε V (G)\S, there exists v ε S such that u, v ε E (G). A dominating set S is called …

Let G be a connected simple graph. A dominating set S⊆ V (G) is a fair dominating set in G if
every two distinct vertices not in S have the same number of neighbors from S, that is, for …