A Novel Bondage Parameter for Network Analysis

TUNÇEL GÖLPEK H.

Symmetry, cilt.17, sa.8, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 8
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/sym17081170
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: graph theory, network design and communications, paired disjunctive domination, paired disjunctive bondage number, trees
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this study, we explore the paired disjunctive domination number—a recently introduced parameter by Henning et al.—within the broader framework of graph and network sensitivity and vulnerability analysis. Building on this concept, we introduce and investigate the paired disjunctive bondage number (PDBN), which measures the minimum number of edge deletions required to increase the paired disjunctive domination number of a graph or its corresponding network model. We begin by computing this new bondage number for several well-known network classes. The focus then shifts to specific families of trees, where we first determine their paired disjunctive domination numbers in detail. Using these values, we calculate the corresponding bondage numbers for various structurally symmetric, hierarchical, and compound tree structures, including double star, comet, double comet, (Formula presented.), and binomial trees, all of which model different types of infrastructural networks. Finally, we present an algorithm for computing PDBN, accompanied by a complexity analysis, and illustrate the practical relevance of the parameter through a case study applying it to a real-life network problem. Our results offer foundational insights into the behavior of this new domination parameter and its bondage variant, contributing to the growing literature on graph vulnerability and suggesting potential applications in the design of resilient and failure-aware networks.