摘要: 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：。
Abstract:
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
Hk,n. We obtain the exact values of
σ-(H3,n),
σ-(H4,n) and
σ-(Hk,k+2). For the remaining case of
Hk,n, we prove an upper bound and a lower bound of its rna number:
.