Roman Domination in Convex Bipartite Graphs

11/17/2021

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by   Sasmita Rout, et al.

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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→{0,1,2} such that for any vertex v∈ V with f(v)=0 must be adjacent to at least one vertex u∈ V with f(u)=2 and ∑_u∈ 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.