An Improved Algorithm for Identification of Dominating Vertex Set in Intuitionistic Fuzzy Graphs

Dominating Critical in Intuitionistic Fuzzy Graphs

Let G be an IFG. Then V D  is said to bae a strong (weak) dominating set if every D V v   is strongly (weakly) dominated by some vertex in D. We denote the strong (weak) intuitionistic fuzzy dominating set by sid-set (wid-set). The minimum vertex cardinality over all the sid-set (wid-set) is called the strong (weak) dominating number of an IFG and is denoted by )] ( [ ) ( G G wid sid   In ...

Dominating Critical in Intuitionistic Fuzzy Graphs

An Improved Algorithm for Parameterized Edge Dominating Set Problem

An edge dominating set of a graph G = (V,E) is a subset M ⊆ E of edges such that each edge in E \ M is incident to at least one edge in M . In this paper, we consider the parameterized edge dominating set problem which asks us to test whether a given graph has an edge dominating set with size bounded from above by an integer k or not, and we design an O(2.2351)-time and polynomial-space algorit...

Improved Approximation Bounds for Edge Dominating Set in Dense Graphs

We analyze the simple greedy algorithm that iteratively removes the endpoints of a maximum-degree edge in a graph, where the degree of an edge is the sum of the degrees of its endpoints. This algorithm provides a 2-approximation to the minimum edge dominating set and minimum maximal matching problems. We refine its analysis and give an expression of the approximation ratio that is strictly less...

An Improved Exact Algorithm for Undirected Feedback Vertex Set

A feedback vertex set in an undirected graph is a subset of vertices removal of which leaves a graph with no cycles. Razgon (SWAT 2006) gave a 1.8899n-time algorithm for finding a minimum feedback vertex set in an n-vertex undirected graph, which is the first exact algorithm for the problem that breaks the trivial barrier of 2. Later, Fomin et al. (Algorithmica 2008) improved the result to 1.75...