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Hk,n的rna数。我们计算出了σ-(H3,n),σ-(H4,n)和σ-(Hk,k+2)的精确值。对于Hk,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 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: .