Abstract
This paper is motivated by the concept of the mixed domination problem on graphs and dedicated to the complexity of variations of the problem such as the signed mixed domination, signed edge domination, minus mixed domination, and minus edge domination problems. In this paper, we present NP-completeness and MAX SNP-hardness results for some of them, and present a general framework of solving these problems and various dominating and covering problems for trees in linear time.
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