AKCE International Journal of Graphs and Combinatorics (Jan 2023)

On balanced cycle domination of graphs

  • Baogen Xu,
  • Ting Lan,
  • Junxia Zhang,
  • Mengmeng Zheng

DOI
https://doi.org/10.1080/09728600.2022.2156309
Journal volume & issue
Vol. 20, no. 1
pp. 47 – 51

Abstract

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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.

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