Disjoint Sets in Graphs and its Application to Electrical Networks

Problem statement: One of the well known problems in Telecommunication and Electrical Power System is how to put Electrical Sensor Unit (ESU) in some various selected locations in the system. Approach: This problem was modeled as the vertex covering problems in graphs. The graph modeling of this problem as the minimum vertex covering set problem. Results: The degree covering set of a graph for every vertex is covered by the set minimum cardinality. The minimu of a graph cardinality of a degree covering set of a graph G is the degree covering number γP(G). Conclusion: We show that Degree Covering Set (DCS) problem is NP-complete. In this study, we also give a linear algorithm to solve the DCS for trees. In addition, we investigate theoretical properties of γP (T) in trees T.