Let G ¼ ðV, EÞ be a simple, undirected, and connected graph. A connected (total) dominating set S V is a secure connected (total) dominating set of G, if for each u 2 V n S, there exists v 2 S such that uv 2 E and ðS n fvgÞ [ fug is a connected (total) dominating set of G. The minimum cardinality of a secure connected (total) dominating set of G denoted by c sc ðGÞðc st ðGÞÞ, is called the secure connected (total) domination number of G. In this paper, we show that the decision problems corresponding to secure connected domination number and secure total domination number are NP-complete even when restricted to split graphs or bipartite graphs. The NP-complete reductions also show that these problems are w[2]-hard. We also prove that the secure connected domination problem is linear time solvable in block graphs and threshold graphs.
Sometimes AI has to deal with incomplete problems. Knowledge Representation is the main component to solve the problems in AI. Various Knowledge representation techniques are available to deal with complete information in Artificial Intelligence. The Knowledge Representation is necessary to deal with incomplete information. Many theories deal with incomplete information is based on Probable (Likelihood) where as fuzzy logic is based on the commonsense and belief. In this paper Fuzzy Knowledge Representation is proposed to deal with the incomplete information. The fuzzy propositions are transformed in to fuzzy modulations and transformed in to Fuzzy Predicate Logic (FPL).The Fuzzy Automated Reasoning is studied using Fuzzy Predicate Logic. The programming in Prolog is given for FPL.
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