奇偶符号Harary图的rna数
The rna Number of Parity Signed Harary Graph

奇偶符号图的概念最初是由Acharya和Kureethara提出的，随后有Zaslavsky等人相继研究。设(G,σ)是n个顶点的符号图，如果能够对(G,σ)中的个顶点等价转换得到(G,+)，则称(G,σ)是一个奇偶符号图，并称σ是G的一个奇偶符号。Σ^-(G)定义为在图G的所有可能奇偶符号σ下，(G,σ)的负边数的集合。图G的rna数σ^-(G)定义为：σ^-(G)=minΣ^-(G)。本文研究了Harary图H_k,n的rna数。我们计算出了σ^-(H_3,n)，σ^-(H_4,n)和σ^-(H_k,k+2)的精确值。对于H_k,n的其他情况，我们给出其rna数的一个上下界：。
The concept of parity signed graphs was initiated by Acharya and Kureethara very recently and then followed by Zaslavsky etc.. Let (G,σ) be a signed graph on n vertices. If (G,σ) is switch-equivalent to (G,+) at a set of many vertices, then we call (G,σ) a parity signed graph and a parity-signature. Σ^-(G) is defined as the set of the number of negative edges of over all possible parity-signatures σ. The rna number σ^-(G) of G is given by σ^-(G)=minΣ^-(G). In this paper, we study the rna number of Harary graph H_k,n. We obtain the exact values of σ^-(H_3,n), σ^-(H_4,n) and σ^-(H_k,k+2). For the remaining case of H_k,n, we prove an upper bound and a lower bound of its rna number: .