| Title: | The 2-rainbow domination number of Cartesian product of cycles |
|---|
| Authors: | ID Brezovnik, Simon (Author)
ID Rupnik Poklukar, Darja (Author)
ID Žerovnik, Janez (Author) |
|---|
| Files: |  AMC_Brezovnik,Rupnik_Poklukar,Zerovnik_2025.pdf (392,01 KB)
MD5: 683BEF037D147D5502B23D0F7375D0A8
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | ZUP - University of Primorska Press
|
|---|
| Abstract: | A k-rainbow dominating function (kRDF) of G is a function that assigns subsets of {1, 2, ..., k} to the vertices of G such that for vertices v with f(v) = ∅ we have
⋃{u ∈ N(v)}f(u) = {1, 2, ..., k}. The weight w(f) of a kRDF f is defined as
w(f) = ∑{v ∈ V(G)}|f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, which is denoted by γrk(G). In this paper, we study the 2-rainbow domination number of the Cartesian product of two cycles. Exact values are given for a number of infinite families and we prove lower and upper bounds for all other cases. |
|---|
| Keywords: | 2-rainbow domination, domination number, Cartesian product |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 16.05.2025 |
|---|
| Publisher: | Založba Univerze na Primorskem |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | 17 str. |
|---|
| Numbering: | Vol. 25, no. 3, [article no.] P3.04 |
|---|
| PID: | 20.500.12556/RUP-21999  |
|---|
| UDC: | 51 |
|---|
| eISSN: | 1855-3974 |
|---|
| DOI: | https://doi.org/10.26493/1855-3974.3168.74d |
|---|
| Publication date in RUP: | 21.10.2025 |
|---|
| Views: | 278 |
|---|
| Downloads: | 5 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
