Exact Resolving Domination Numbers of Wheel-Derived Graphs With an ILP Formulation

M. Valentina Gladia, V. Jude Annie Cynthia and Anthuvan Joseph Benjamin

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-15

Abstract: Let G=V,E be a simple, connected graph, and let da,g denote the shortest distance between vertices a and g. An ordered subset R of V, with R=k and k∈N, is known as a resolving set if, for m≠c,∃t∈R such that dm,t≠dc,t, ∀m, c ∈ V–R. The distance code representation for b∈V−R w.r.t. R is given by codeb∣R=db,t1,…,db,tk, ∀ ti ∈ R. A dominating set D satisfies the condition that ∀w∈V−D is adjacent to at least one vertex within D. A resolving dominating set (RDS) R′⊆V guarantees both conditions, and the smallest cardinality among all RDS is termed as resolving domination number, denoted by γresG. We determine γres for several wheel-derived graph families, including water wheel graphs, closed water wheel graphs, sunflower graphs, and flower graphs, and obtain exact values for these graph classes. In addition, we develop an exact integer linear programming (ILP) formulation for the minimum RDS problem on arbitrary simple connected graphs. The formulation employs binary decision variables and linear domination and resolvability constraints, providing a general, exact optimization model that complements the theoretical results established for the wheel-derived graph families.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ijmms/2026/7334438.pdf (application/pdf)
http://downloads.hindawi.com/journals/ijmms/2026/7334438.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:7334438

DOI: 10.1155/ijmm/7334438

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().