Name
Abstract | ||
|---|---|---|
A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The total domination number @c"t(G) is the minimum cardinality of a total dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we investigate relationships between the annihilation number and the total domination number of a graph. Let T be a tree of order n=2. We show that @c"t(T)@?a(T)+1, and we characterize the extremal trees achieving equality in this bound. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.dam.2012.09.006 | Discrete Applied Mathematics |
Keywords | Field | DocType |
order n,total domination number,largest integer k,extremal tree,non-decreasing degree sequence,graph g,annihilation number,k term,minimum cardinality | Integer,Discrete mathematics,Graph,Combinatorics,Dominating set,Vertex (geometry),Annihilation,Cardinality,Degree (graph theory),Domination analysis,Mathematics | Journal |
Volume | Issue | ISSN |
161 | 3 | 0166-218X |
Citations | PageRank | References |
6 | 0.53 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wyatt J. Desormeaux | 1 | 44 | 8.26 |
| Teresa W. Haynes | 2 | 774 | 94.22 |
| Michael A. Henning | 3 | 1865 | 246.94 |