Graph Theory: Lecture No. 7
A set S⊆V(G)is a dominating set if every
vertex not in Shas a neighbour in S. The
domination number γ(G)is the minimum size
of a dominating set in G.
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Dominating Set - Graph Theory - Lecture Slides, Slides of Design and Analysis of Algorithms
The major points which I found very interactive in learning graph theory are:Dominating Set, Neighbour, Vertex, Minimum Size, Isolated Vertices, Vertex Graph, Minimum Degree, Cardinality, Independent Set, Claw Free Graph
Typology: Slides
2012/2013
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A set S ⊆ V (G ) is a dominating set if every vertex not in S has a neighbour in S. The domination number γ(G ) is the minimum size of a dominating set in G.
If there are no isolated vertices in G , then γ(G ) ≤ β(G ).
A set of vertices in a graph is an independent dominating set if and only if it is a maximal independent set.
Every claw free graph has an independent dominating set of size γ(G ).
Every directed graph G has a path cover P and independent set {vP : P ∈ P} of vertices such that vP ∈ P for every P ∈ P.
In every finite partially ordered set (P, ≤), the minimum number of chains with union P is equal to the maximum cardinality of an antichain in P.