Paper Info
Title
Perfect graphs involving semitotal and semipaired domination.
Abstract
Let be a graph with vertex set and no isolated vertices, and let be a dominating set of . The set is a semitotal dominating set of if every vertex in is within distance 2 of another vertex of . And, is a semipaired dominating set of if can be partitioned into 2-element subsets such that the vertices in each 2-set are at most distance two apart. The semitotal domination number is the minimum cardinality of a semitotal dominating set of , and the semipaired domination number is the minimum cardinality of a semipaired dominating set of . For a graph without isolated vertices, the domination number , the total domination , and the paired domination number are related to the semitotal and semipaired domination numbers by the following inequalities: and . Given two graph parameters and related by a simple inequality for every graph having no isolated vertices, a graph is -perfect if every induced subgraph with no isolated vertices satisfies . Alvarado et al. (Discrete Math 338:1424–1431, ) consider classes of -perfect graphs, where and are domination parameters including , and . We study classes of perfect graphs for the possible combinations of parameters in the inequalities when and are included in the mix. Our results are characterizations of several such classes in terms of their minimal forbidden induced subgraphs.
Year
DOI
Venue
2018
https://doi.org/10.1007/s10878-018-0303-9
J. Comb. Optim.
Keywords
Field
DocType
Paired-domination,Perfect graphs,Semipaired domination,Semitotal domination,05C69
Graph,Dominating set,Combinatorics,Two-graph,Vertex (geometry),Cardinality,Induced subgraph,Domination analysis,Mathematics
Journal
Volume
Issue
ISSN
36
2
1382-6905
Citations 
PageRank 
References 
0
0.34
6
Authors
2
Name
Order
Citations
PageRank
Teresa W. Haynes177494.22
Michael A. Henning21865246.94