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...

An independent dominating set of the simple graph G=(V,E) is a vertex subset that both and in G. The domination polynomial G Di(G,x)=∑Ax|A|, summed over all subsets A⊆V. A root Di(G,x) called an independence root. We investigate polynomials some generalized compound graphs. As consequence, we construct graphs whose roots are real. Also, consider related to paths study number their sets.

A double Roman dominating function of a graph $G$ is $f:V(G)\rightarrow \{0,1,2,3\}$ having the property that for each vertex $v$ with $f(v)=0$, there exists $u\in N(v)$ $f(u)=3$, or are $u,w\in $f(u)=f(w)=2$, and if $f(v)=1$, then adjacent to assigned at least $2$ under $f$. The domination number $\gamma_{dR}(G)$ minimum weight $f(V(G))=\sum_{v\in V(G)}f(v)$ among all functions $G$. An outer i...

During the last thirty years, the concept of domination in graphs has generated an impressive interest. A recent bibliography on the subject contains more than 1200 references and the number of new definitions is continually increasing. Rather than trying to give a catalogue of all of them, we survey the most classical and important notions (as independent domination, irredundant domination, k-...