Abstract
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.
Highlights
Let P ⊆ V be the set of vertices where the Electrical Sensor Unit (ESU) are placed: the state of the system can be decided from a set of measurements
We investigate about linear time algorithm to find a Degree Covering Set (DCS) in trees and study theoretical properties of the degree covering number in trees
If |S| = 1, vertex, Kj,1 or Kj,2 and P is a DCS of size at most k = n. renaming u and v if necessary, we may assume that no we must show that if G(K) has a DCS vertex in the maximum subtree Tu rooted at u belongs of size at most k = n, K has a satisfying truth to S
Summary
The other finding rules are as follows: At this moment we are dependable with the electivity power. The consumption of electricity is increasing every year. The electric power industries have to monitor carefully their system’s state periodically as. We observed the incidences of vertices to edges We observed joining any edges defined by a set of state variables (Ramos and Tahan, 2009; Kumkratug, 2010; Osuwa and Igwiro, 2010).
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