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| Content Provider | Society for Industrial and Applied Mathematics (SIAM) |
|---|---|
| Author | Haynes, Teresa W. Hedetniemi, Sandra M. Hedetniemi, Stephen T. Henning, Michael A. |
| Copyright Year | 2002 |
| Abstract | The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graphs. We consider the graph theoretical representation of this problem as a variation of the dominating set problem and define a set S to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph G is the power domination number $\gamma_P(G)$. We show that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs. On the other hand, we give a linear algorithm to solve the PDS for trees. In addition, we investigate theoretical properties of $\gamma_P(T)$ in trees T. |
| Starting Page | 519 |
| Ending Page | 529 |
| Page Count | 11 |
| File Format | |
| ISSN | 08954801 |
| DOI | 10.1137/S0895480100375831 |
| e-ISSN | 10957146 |
| Journal | SIAM Journal on Discrete Mathematics (SJDMEC) |
| Issue Number | 4 |
| Volume Number | 15 |
| Language | English |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher Date | 2006-08-01 |
| Access Restriction | Subscribed |
| Subject Keyword | domination power domination Dominating sets, independent sets, cliques electric power monitoring |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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