Back to Search
Start Over
The k-Power Domination Number in Some Self-Similar Graphs
- Publication Year :
- 2019
-
Abstract
- The $k$-power domination problem is a problem in graph theory, which has applications in many areas. However, it is hard to calculate the exact $k$-power domination number since determining k-power domination number of a generic graph is a NP-complete problem. We determine the exact $k$-power domination number in two graphs which have the same number of vertices and edges: pseudofractal scale-free web and Sierpi\'nski gasket. The $k$-power domination number becomes 1 for $k\ge2$ in the Sierpi\'nski gasket, while the $k$-power domination number increases at an exponential rate with regard to the number of vertices in the pseudofractal scale-free web. The scale-free property may account for the difference in the behavior of two graphs.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1911.08045
- Document Type :
- Working Paper