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Total domination in graphs with minimum degree three
Author(s) -
Favaron Odile,
Henning Michael A.,
Mynhart Christina M.,
Puech Joël
Publication year - 2000
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(200005)34:1<9::aid-jgt2>3.0.co;2-o
Subject(s) - combinatorics , mathematics , dominating set , domination analysis , vertex (graph theory) , graph , degree (music) , discrete mathematics , bound graph , graph power , line graph , physics , acoustics
A set S of vertices of a graph G is a total dominating set, if every vertex of V ( G ) is adjacent to some vertex in S . The total domination number of G , denoted by γ t ( G ), is the minimum cardinality of a total dominating set of G . We prove that, if G is a graph of order n with minimum degree at least 3, then γ t ( G ) ≤ 7 n /13. © 2000 John Wiley & Sons, Inc. J Graph Theory 34:9–19, 2000