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Total domination in graphs
Author(s) -
Cockayne E. J.,
Dawes R. M.,
Hedetniemi S. T.
Publication year - 1980
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230100304
Subject(s) - dominating set , combinatorics , mathematics , vertex (graph theory) , partition (number theory) , domination analysis , undirected graph , graph , discrete mathematics
A set D of vertices of a finite, undirected graph G = ( V, E ) is a total dominating set if every vertex of V is adjacent to some vertex of D . In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number of G (the largest order of a partition of G into total dominating sets).