Neutrosophic graph (NG) is a powerful tool in theory, which capable of modeling many real-life problems with uncertainty due to unclear, varying, and indeterminate information. Meanwhile, the fuzzy graphs (FGs) intuitionistic (IFGs) may not handle these as efficiently NGs. It difficult model imprecise information vagueness real-world scenarios. Many optimization are modeled solved using well-kn...

Let γ(G) be the domination number of a graph G. It is shown that for any k ≥ 0 there exists a Cartesian graph bundle B φF such that γ(B φF ) = γ(B)γ(F )−2k. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing’s conjecture on strong graph bundles is shown not to be true by proving the inequ...

The existence of a constant time algorithm for solving different domination problems on the subclass of polygraphs, rotagraphs and fasciagraphs, is shown by means of path algebras. As these graphs include products (the Cartesian, strong, direct, lexicographic) of paths and cycles, we implement the algorithm to get formulas in the case of the domination numbers, the Roman domination numbers and ...

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number γP (G) of G is the minimum cardinality of a power dominating set. Dorfling and Henning [2] determined the power domination number of the Cartesian product of paths. I...

A Roman dominating function (RD-function) on a graph G = ( V , E ) is f : → {0, 1, 2} satisfying the condition that every vertex u for which 0 adjacent to at least one v 2. An in perfect (PRD-function) if with exactly The (perfect) domination number γ R p )) minimum weight of an . We say strongly equals ), denoted by ≡ γR RD-function PRD-function. In this paper we show given it NP-hard decide w...