A study on parity signed graphs: The rna number

作者：

Highlights：

• The paper confirms the conjecture by Acharya and Kureethara [1] that for any graph G, ∑−(G)={σ−(G)} if and only if G is K1,n−2 with n even orKn.

• The paper proves a nontrivial upper bound for the rna number of a graph and characterizes the equality case.

• The paper applies so-called parity-switching to study the rna number for the first time.

• The paper answers a question on parity complement, proposed by Acharya et al. [2].

摘要

•The paper confirms the conjecture by Acharya and Kureethara [1] that for any graph G, ∑−(G)={σ−(G)} if and only if G is K1,n−2 with n even orKn.•The paper proves a nontrivial upper bound for the rna number of a graph and characterizes the equality case.•The paper applies so-called parity-switching to study the rna number for the first time.•The paper answers a question on parity complement, proposed by Acharya et al. [2].

论文关键词：Parity signed graphs,The rna number,Parity-switching,Degree-balance

论文评审过程：Received 17 December 2021, Revised 8 June 2022, Accepted 10 June 2022, Available online 23 June 2022, Version of Record 23 June 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127322