Roman Domination in Convex Bipartite Graphs

Abstract

In the Roman domination problem, an undirected simple graph $G(V,E)$ is given. The objective of Roman domination problem is to find a function $f:V\to \{0,1,2\}$ such that for any vertex $v\in V$ with $f(v)=0$ must be adjacent to at least one vertex $u\in V$ with $f(u)=2$ and ${\sum }_{u\in V}f(u)$, called Roman domination number, is minimized. It is already proven that the Roman domination problem (RDP) is NP-complete for general graphs and it remains NP-complete for bipartite graphs. In this paper, we propose a dynamic programming based polynomial time algorithm for RDP in convex bipartite graph.

The authors have withdrawn this version due to an error in the algorithm that invalidates the main results