On balanced cycle domination of graphs

• Published in: AKCE international journal of graphs and combinatorics Vol. 20; no. 1; pp. 47 - 51
• Main Authors: Xu, Baogen, Lan, Ting, Zhang, Junxia, Zheng, Mengmeng
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 02.01.2023
• Subjects: Balanced cycle domination number; signed cycle balanced domination number; signed cycle balanced graph
• ISSN: 0972-8600; 2543-3474
• DOI: 10.1080/09728600.2022.2156309

AbstractLet [Formula: see text] be a graph. A function [Formula: see text] is said to be a balanced cycle dominating function (BCDF) of [Formula: see text] if [Formula: see text] holds for any induced cycle [Formula: see text] of [Formula: see text] The balanced cycle domination number of [Formula: see text] is defined as [Formula: see text] A graph [Formula: see text] is said to be a signed cycle balanced graph (SCB-graph) if there exists a function [Formula: see text] such that [Formula: see text] holds for any induced cycle [Formula: see text] of [Formula: see text] and [Formula: see text] is said to be a signed cycle balanced dominating function (SCBDF) of [Formula: see text] The signed cycle balanced domination number of [Formula: see text] is defined as [Formula: see text] In this paper, we present upper bounds for balanced cycle domination number and signed cycle balanced domination number. The exact values of this parameter are determined for a few classes of graphs.