Abstract We describe a simple deterministic $$O( \varepsilon ^{-1} \log \Delta )$$ O ( ε - 1 log Δ ) round distributed algorithm for $$(2\alpha +...

Bipolar intuitionistic fuzzy graphs (BIFG) with perfectly connected domination are introduced in this study. The study also discusses the bipolar antifuzzy (BIAFG) concepts. Additionally, topic of 2-domination BIAFG explored. we developed secure edge dominating set and its number some results derived suitable examples.

A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in cite{bhh} as a function$f:V(G)rightarrow{0,1,2,3}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least twoneighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$, and if $f(v)=1$, then the vertex $v$ must haveat least one neighbor $u$ with $f(u)ge 2$. The weight of a double R...

The investigation of impact of fuzzy sets on zero forcing set is the main aim of this paper. According to this, results lead us to a new concept which we introduce it as Fuzzy Zero Forcing Set (FZFS). We propose this concept and suggest a polynomial time algorithm to construct FZFS. Further more we compute the propagation time of FZFS on fuzzy graphs. This concept can be more efficient to model...

We present the first polynomial time algorithms for solving the NPcomplete graph problems DOMINATING SET and TOTAL DOMINATING SET when restricted to asteroidal triple-free graphs. We also present algorithms to compute a minimum cardinality dominating set and a minimum cardinality total dominating set on a large superclass of the asteroidal triple-free graphs, called DDP-graphs. These algorithms...