A linear time algorithm for weighted k-fair domination problem in cactus graphs

Novak, Tina (author), Žerovnik, Janez (author)

A set D of vertices in a graph G is a k-fair dominating set if every vertex not in D is adjacent to exactly k vertices in D. The weighted k-fair domination number ▫$wfd_k(G)$▫ of a vertex-weighted graph G is the minimum weight w(D) among all k-fair dominating sets D. In addition to the weighted k-fair domination number, some auxiliary parameters are defined. It is shown that for a cactus graph, the weighted k-fair domination number and auxiliary parameters can be calculated in linear time.

• Language: English
• Keywords: linear algorithms, cactus graphs, DFS structure, weighted k-fair domination
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Publication date: 02.09.2022
• Year: 2022
• Number of pages: 22 str.
• Numbering: Vol. 3, iss. 3, art. 46
• PID: 20.500.12556/RUL-139679
• UDC: 519.17
• ISSN on article: 2662-2556
• DOI: 10.1007/s43069-022-00154-8
• COBISS.SI-ID: 120314883
• Publication date in RUL: 06.09.2022

Record is a part of a journal

• Title: Operations research forum
• Shortened title: SN Oper. Res. Forum
• Publisher: Springer
• ISSN: 2662-2556
• COBISS.SI-ID: 120299011

Secondary language

• Language: Slovenian
• Keywords: linearni algoritmi, kaktus grafi, DFS strukture, neodvisna dominacija, teorija grafov