Work

The 2-rainbow domination number of Cartesian bundles over cycles

Year: 2024

Type: article

Abstract: A k-rainbow dominating function (kRDF) f of G assigns subsets of $$\{1,2,\ldots ,k\}$$ to vertices, such that for vertex v with $$f(v)=\emptyset$$ , $$\bigcup \nolimits _{u\in N(v)}f(u)=\{1,2,\ldots ,k\}$$ . The weight w(f) of kRDF f is $$w(f)=\sum _{v\in V(G)}\left| f(v)\right|$$ . The minimum weight of a kRDF of G is the k-rainbow domination number denoted by $$\gamma _{rk}(G)$$ . This paper focuses on the 2-rainbow domination number of Cartesian graph bundles of cycles over cycles, extending recent results for Cartesian product of cycles. Exact values are given for certain infinite families, and tight lower and upper bounds are established for general case.

Source: Central European Journal of Operations Research

DOI: 10.1007/s10100-024-00949-6

Authors: Simon Brezovnik, Darja Rupnik Poklukar, Janez Žerovnik

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics, Rudolfovo – Science and Technology Centre Novo mesto

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funder: Javna Agencija za Raziskovalno Dejavnost RS