Each vertex in Q n is represented by a n -tuple with 0's and 1's. Livingston, Characterization of trees with equal domination and independent domination numbers, Congr. Well covered generalized Petersen graphs Hence it remains to show that D is of minimum cardinality. Thus i and ii are obvious. Staples, On some subclasses of well-covered graphs, J.
Some Toughness Results In Independent Domination Critical Graphs
Nieminen, Two bounds for the domination number of a graph, J. Farber, Domination, independent domination, and duality in strongly chordal graphs, Discrete Appl. Moon, Relations between packing and covering numbers of a tree, Pacific J. Hence it remains to show that D is of minimum cardinality. Nowakowski, A characterization of well covered graphs of girth 5 or greater, J.
On locating independent domination number of amalgamation graphs - IOPscience
Zverovich, A characterization of domination perfect graphs, J. Volkmann, On packing and covering numbers of graphs, ibid. Stewart, Dominating sets in perfect graphs, Discrete Math. Theory 8 , Johnson, Computers and Intractability: The n -dimensional cube or hypercube Q n contains 2 n vertices and is n -regular.
This is a contradiction to the maximality of I. Plummer, On well-covered 3-polytopes, Ars Combin. Also D is of minimum cardinality in G. Motivated by Observation 1. Roberts, On graphs having domination number half their order, Period.