Edge Criticality in Graph Domination

  title={Edge Criticality in Graph Domination},
  author={Jan H. van Vuuren},
  journal={Graphs and Combinatorics},
  • 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
The cost of edge removal in graph domination


The bondage number of a graph
Domination alteration sets in graphs
Complexity of Bondage and Reinforcement
This paper shows that the decision problems for bondage, total bondage and reinforcement are all NP-hard.
Domination in graphs : advanced topics
LP-duality, complementarity and generality of graphical subset parameters dominating functions in graphs fractional domination and related parameters majority domination and its generalizations
Fundamentals of domination in graphs
Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of
Theory of Graphs
Fundamental concepts Connectedness Path problems Trees Leaves and lobes The axiom of choice Matching theorems Directed graphs Acyclic graphs Partial order Binary relations and Galois correspondences
A characterisation of trees in which no edge is essential to the domination number
  • Ars Comb. 33, 65–76
  • 1992