Two Short Proofs on Total Domination

• Autorzy: Allan Bickle
• Języki publikacji: EN

Abstrakty

EN

A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set. We provide a short proof of the result that Υt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.

Słowa kluczowe

EN

total domination

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 457-459

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

Allan Bickle

• Department of Mathematics Western Michigan University 1903 W. Michigan Kalamazoo, MI 49008

Bibliografia

• [1] R.C. Brigham, J.R. Carrington and R.P. Vitray, Connected graphs with maximum total domination number , J. Combin. Comput. Combin. Math. 34 (2000) 81-96.
• [2] E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219. doi:10.1002/net.3230100304
• [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc, 1998).

Identyfikatory

DOI

10.7151/dmgt.1655