Total domination in interval graphs
Information Processing Letters
Efficient Algorithms for the Domination Problems on Interval and Circular-Arc Graphs
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A linear time recognition algorithm for proper interval graphs
Information Processing Letters
Networks
| Hi-index | 0.89 |
Let G=(V,E) be a graph without isolated vertices and having at least 3 vertices. A set L@?V(G) is a liar@?s dominating set if (1) |N"G[v]@?L|=2 for all v@?V(G), and (2) |(N"G[u]@?N"G[v])@?L|=3 for every pair u,v@?V(G) of distinct vertices in G, where N"G[x]={y@?V|xy@?E}@?{x} is the closed neighborhood of x in G. Given a graph G and a positive integer k, the liar@?s domination problem is to check whether G has a liar@?s dominating set of size at most k. The liar@?s domination problem is known to be NP-complete for general graphs. In this paper, we propose a linear time algorithm for computing a minimum cardinality liar@?s dominating set in a proper interval graph. We also strengthen the NP-completeness result of liar@?s domination problem for general graphs by proving that the problem remains NP-complete even for undirected path graphs which is a super class of proper interval graphs.