Abstract
A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to a vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. Much interest in total domination in graphs has arisen from a computer program Graffiti.pc that has generated several hundred conjectures on total domination (see http://cms.dt.uh.edu/faculty/delavinae/research/wowII). We prove and disprove some conjectures from Graffiti.pc concerning lower bounds on the total domination number of a graph.
| Original language | English |
|---|---|
| Pages (from-to) | 52-66 |
| Number of pages | 15 |
| Journal | Journal of Combinatorial Optimization |
| Volume | 31 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2016 |
Keywords
- Graffiti.pc conjectures
- Total domination
- Total domination number
ASJC Scopus subject areas
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics