变换图的正则性和谱半径

Regularity and Spectral Radius of Transformation Graphs

在前人对八种变换图研究的基础上,探讨了变换后满足正则性的原图的性质,得到了如下结果:G^(+++)及G^(---)是正则图当且仅当G是正则图;G^(++-)和G^(--+)为正则图的充要条件是G为C_n、K_(2,n-2)或K_4;G^(+-+)和G^(-+-)是正则图当且仅当G为C_5、K_7、K_2、K_(3,3)或G_0;G^(-++)和G^(+--)是正则的当且仅当G是(n-1)/2-正则图．同时还讨论了变换图的谱半径上界,并对这些上界进行了估计．

In this Paper, we study the graphs which can be transformed to regular graphs. We present the results： G^＋＋＋ and G^--- are regular if and only if G is regular; G^＋＋- and G^--＋ are regular if and only if G≌ Cn or K2,n-2 or K4; G^＋-＋ and G^-＋- are regular if and only if G ≌ C5 or K7 or K2 or K3,3 or G0; G^-＋＋ and G^＋-- are regular if and only if G is （n-1）/2-regular. We also give some upper bounds on the spectral.radius of transformation graphs. Then we estimate these upper bounds.