Paired disjunctive domination in some shadow distance graphs

Golpek H. T., Aytac A.

Discrete Mathematics, Algorithms and Applications, 2025 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s1793830925500788
  • Dergi Adı: Discrete Mathematics, Algorithms and Applications
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: Paired domination, paired disjunctive domination, shadow graph, graph vulnerability
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

This paper investigates the concept of paired disjunctive domination, initially proposed by Henning et al. A subset D ⊆ V is defined as a disjunctive dominating set of a graph G if, for every vertex v ∈ V, there exists either a vertex in D adjacent to v, or there are at least two vertices in D such that their distance from v is exactly two in G. Furthermore, a disjunctive dominating set D ⊆ V is labeled as a paired disjunctive dominating set if the induced subgraph by D in G contains a perfect matching. This paper explores the implications of the paired disjunctive domination parameter on shadow graphs, 2-distance graphs, and 3-distance path and cycle shadow graphs.