# Algorithmic aspects of certified domination in graphs

Document Type : Original paper

Authors

1 IcfaiTech (Faculty of Science &amp;amp;amp;amp; Technology) ICFAI Foundation for Higher Education, Hyderabad, India

2 Director (n-CARDMATH) Kalasalingam University Anand Nagar, Krishnankoil-626 126 Tamil Nadu, India

3 Department of Computer Science and Engineering, National Institute of Technology Warangal, Telangana, India

4 National Institute of Technology Warangal

Abstract

A dominating set $D$ of a graph $G=(V,E)$ is called a certified dominating set of $G$ if $\vert N(v) \cap (V \setminus D)\vert$ is either 0 or at least 2 for all $v \in D$. The certified domination number $\gamma_{cer}(G)$ is the minimum cardinality of a certified dominating set of $G$. In this paper, we prove that the decision problem corresponding to $\gamma_{cer}(G)$ is NP-complete for split graphs, star convex bipartite graphs, comb convex bipartite graphs and planar graphs. We also prove that it is linear time solvable for chain graphs, threshold graphs and bounded tree-width graphs.

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