Extremal mixed metric dimension with respect to the cyclomatic number

作者：

Highlights：

• Prove that for unbalanced Θ-graphs the strict inequality holds.

• Prove that for balanced Θ-graphs the equality is attained.

• Further conjecture that balanced Θ-graphs, besides trees and cactus graph in which every cycle has precisely one vertex of degree ≥ 3 for which it was already known that equality holds, are the only graphs for which this upper bound is attained.

摘要

•Prove that for unbalanced Θ-graphs the strict inequality holds.•Prove that for balanced Θ-graphs the equality is attained.•Further conjecture that balanced Θ-graphs, besides trees and cactus graph in which every cycle has precisely one vertex of degree ≥ 3 for which it was already known that equality holds, are the only graphs for which this upper bound is attained.

论文关键词：

论文评审过程：Received 15 December 2020, Revised 20 March 2021, Accepted 24 March 2021, Available online 3 April 2021, Version of Record 3 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126238