(C3, C4, C5, C7)-Free Almost Well-Dominated Graphs

Alizadeh H., Gözüpek D., Ekinci G. B.

Discussiones Mathematicae - Graph Theory, vol.42, no.4, pp.1099-1117, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.7151/dmgt.2331
  • Journal Name: Discussiones Mathematicae - Graph Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.1099-1117
  • Keywords: well-dominated graphs, almost well-dominated graphs, domination gap, COVERED GRAPHS
  • Kocaeli University Affiliated: No

Abstract

© 2020 Hadi Alizadeh et al., published by Sciendo.The domination gap of a graph G is defined as the di erence between the maximum and minimum cardinalities of a minimal dominating set in G. The term well-dominated graphs referring to the graphs with domination gap zero, was first introduced by Finbow et al. [Well-dominated graphs: A collection of well-covered ones, Ars Combin. 25 (1988) 5-10]. In this paper, we focus on the graphs with domination gap one which we term almost well-dominated graphs. While the results by Finbow et al. have implications for almost well-dominated graphs with girth at least 8, we extend these results to (C3, C4, C5, C7)-free almost well-dominated graphs by giving a complete structural characterization for such graphs.