Semitotal domination versus domination and total domination in trees
Copyright policy )Semitotal domination versus domination and total domination in trees
A set S of vertices in G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, γt2(G), is the minimum cardinality of a semitotal dominating set of G. Clearly, γ(G) ≤ γt2(G) ≤ γt(G). In this paper, for any nontrivial tree T that is not a star, we investigate the ratios γt2(T )/γ(T) and γt(T )/γt2(T), and provide constructive characterizations of trees achieving the upper bounds.
- Xiamen University of Technology China (People's Republic of)
Graph labelling (graceful graphs, bandwidth, etc.), semitotal domination number, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), total domination number, domination number
Graph labelling (graceful graphs, bandwidth, etc.), semitotal domination number, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), total domination number, domination number
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!