The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Domination in Graphs Applied to Electric Power Networks
SIAM Journal on Discrete Mathematics
The bottleneck independent domination on the classes of bipartite graphs and block graphs
Information Sciences—Informatics and Computer Science: An International Journal
Graph Theory With Applications
Graph Theory With Applications
Restricted power domination and fault-tolerant power domination on grids
Discrete Applied Mathematics
On the power domination number of the generalized Petersen graphs
Journal of Combinatorial Optimization
Generalized power domination of graphs
Discrete Applied Mathematics
| Hi-index | 5.23 |
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 domination problem in graphs. In 2002, Haynes et al. considered the graph theoretical representation of this problem as a variation of the domination problem. They defined 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 power domination number γp(G) of a graph G is the minimum cardinality of a power dominating set of G. This problem was proved NP-complete even when restricted to bipartite graphs and chordal graphs. In this paper, we present a linear time algorithm for solving the power domination problem in block graphs. As an application of the algorithm, we establish a sharp upper bound for power domination number in block graphs and characterize the extremal graphs.