Dominating pair graphs

Jitender S Deogun, Dieter Kratsch

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A pair of vertices of a graph is called a dominating pair if the vertex set of every path between these two vertices is a dominating set of the graph. A graph is a weak dominating pair graph if it has a dominating pair. Further, a graph is called a dominating pair graph if each of its connected induced subgraphs is a weak dominating pair graph Dominating pair graphs form a class of graphs containing interval, permutation, cocomparability, and asteroidal triple-free graphs. Our purpose is to study the structural properties of dominating pair graphs. Our main results are a polar theorem for the dominating pairs in weak dominating pair graphs and an existence theorem for minimum cardinality connected dominating sets that induce a simple path in connected dominating pair graphs of diameter riot equal to three. Furthermore, we present a forbidden induced subgraph characterization of chordal dominating pair graphs.

Original languageEnglish (US)
Pages (from-to)353-366
Number of pages14
JournalSIAM Journal on Discrete Mathematics
Volume15
Issue number3
DOIs
StatePublished - May 1 2002

Fingerprint

Structural properties
Graph in graph theory
Forbidden Induced Subgraph
Connected Dominating Set
Path
Interval Graphs
Dominating Set
Induced Subgraph
Vertex of a graph
Structural Properties
Existence Theorem
Cardinality
Permutation

Keywords

  • Algorithms
  • Asteroidal triple-free graphs
  • Dominating pair graphs
  • Graph classes

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Dominating pair graphs. / Deogun, Jitender S; Kratsch, Dieter.

In: SIAM Journal on Discrete Mathematics, Vol. 15, No. 3, 01.05.2002, p. 353-366.

Research output: Contribution to journalArticle

Deogun, Jitender S ; Kratsch, Dieter. / Dominating pair graphs. In: SIAM Journal on Discrete Mathematics. 2002 ; Vol. 15, No. 3. pp. 353-366.
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