Total Domination in Graphs With Diameter 2
Document Type
Article
Publication Date
1-1-2014
Description
The total domination number γt(G) of a graph G is the minimum cardinality of a set S of vertices, so that every vertex of G is adjacent to a vertex in S. In this article, we determine an optimal upper bound on the total domination number of a graph with diameter 2. We show that for every graph G on n vertices with diameter 2, γt(G)≤1+nln(n). This bound is optimal in the sense that given any ε>0, there exist graphs G with diameter 2 of all sufficiently large even orders n such that γt(G)>(14+ε)nln(n).
Citation Information
Desormeaux, Wyatt J.; Haynes, Teresa W.; Henning, Michael A.; and Yeo, Anders. 2014. Total Domination in Graphs With Diameter 2. Journal of Graph Theory. Vol.75(1). 91-103. https://doi.org/10.1002/jgt.21725 ISSN: 0364-9024