For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for ...

For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for ...

Let G be a graph of order n ≥ 2 and n1, n2, .., nk be integers such that 1 ≤ n1 ≤ n2 ≤ .. ≤ nk and n1 + n2 + .. + nk = n. Let for i = 1, .., k: Ai ⊆ Kni where Km is the set of all pairwise non-isomorphic graphs of order m, m = 1, 2, ... In this paper we study when for a domination related parameter μ (such as domination number, independent domination number and acyclic domination number) is ful...

A dominating set D of an IFG G = (V, E) is a non-split dominating set, if the induced intuitionistic fuzzy subgraph 〈ܸ − ‫〉ܦ‬ is connected. The Non-split domination number ߛ ௡௦ ሺ‫ܩ‬ሻ of IFG G is the minimum cardinality of all Non-split dominating set. In this paper we study some theorems in Non-split dominating sets of IFG and some results of ߛ ௡௦ ሺ‫ܩ‬ሻwith other known parameters of IFG G. 1. In...

For any graph G and a set ~ of graphs, two distinct vertices of G are said to be ~-adjacent if they are contained in a subgraph of G which is isomorphic to a member of ~. A set S of vertices of G is an ~-dominating set (total ~¢~-dominating set) of G if every vertex in V(G)-S (V(G), respectively) is 9¢g-adjacent to a vertex in S. An ~-dominating set of G in which no two vertices are oCf-adjacen...

Supergrid graphs are derived by computing stitch paths for computerized embroidery machines. In the past, we have studied Hamiltonian-related properties of supergrid and their subclasses graphs. this paper, propose a generalized graph class called extended Extended include grid graphs, diagonal triangular as study problems domination independent on A dominating set is subset vertices it, such t...

a {em roman dominating function} on a graph $g$ is a function$f:v(g)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}a {em restrained roman dominating}function} $f$ is a {color{blue} roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} the wei...

for any $k in mathbb{n}$, the $k$-subdivision of graph $g$ is a simple graph $g^{frac{1}{k}}$, which is constructed by replacing each edge of $g$ with a path of length $k$. in [moharram n. iradmusa, on colorings of graph fractional powers, discrete math., (310) 2010, no. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $g$ has been introduced as a fractional power of $g$, denoted by ...