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A Characterization of Domination Reducible Graphs

✍ Scribed by Igor Ed. Zverovich

Publisher: Springer Japan
Year: 2004
Tongue: English
Weight: 274 KB
Volume: 20
Category: Article
ISSN: 0911-0119
DOI: 10.1007/s00373-003-0541-0

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Let u(G) and i(G) be the domination number and independent domination number of a graph G. respectively. Sumner and Moore [8] define a graph G to be domination perfect if y( H) = i( H), for every induced subgraph H of G. In this article, we give a finite forbidden induced subgraph characterization o

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Let β(G) and Γ(G) be the independence number and the upper domination number of a graph G, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. The class of Γ-perfect graphs generalizes such well-known classes of graphs as strongly perfect graphs, absorbantl

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Let G be a simple graph of order n(G). A vertex set D of G is dominating if every vertex not in D is adjacent to some vertex in D, and D is a covering if every edge of G has at least one end in D. The domination number 7(G) is the minimum order of a dominating set, and the covering number/~(G) is th