Edge Criticality in Graph Domination

@article{Vuuren2016EdgeCI,
  title={Edge Criticality in Graph Domination},
  author={Jan H. van Vuuren},
  journal={Graphs and Combinatorics},
  year={2016},
  volume={32},
  pages={801-811}
}
  • J. V. Vuuren
  • Published 1 March 2016
  • Mathematics
  • Graphs and Combinatorics
A vertex subset $$D\subseteq V$$D⊆V of a graph $$G=(V,E)$$G=(V,E) is a dominating set of G if each vertex of G is a member of D or is adjacent to a member of D. The cardinality of a smallest dominating set of G is called the domination number of G and a nonempty graph G is q-critical if q is the smallest number of arbitrary edges of G whose removal from Gnecessarily increases the domination number of the resulting graph. The classes of q-critical graphs of order n are characterised in this… 
Total domination polynomials of graphs
Given a graph $G$, a total dominating set $D_t$ is a vertex set that every vertex of $G$ is adjacent to some vertices of $D_t$ and let $d_t(G,i)$ be the number of all total dominating sets with size
The cost of edge removal in graph domination
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