【摘要】 本文构造了一类链状正则图G_k∶δ,求出了它们的平均距离D(G_k.δ),并得到关系式上式等号成立当且仅当δ=4f且k=0.这个估计式指出了施容华猜想[1]D(G)≤n/(δ+1)不成立. 文中进一步证明了这一类链状正则图有最大的直径,所以可以作出猜想: 若G是n阶连通图,则D(G)<(n+1)/(δ+1),其中δ是图G的最小度。更多还原

【Abstract】 In this paper the authors construct a kind of chain regular graphs, dan prove that their average distances D(G_k:δ satisfy:（n/（δ））≤D(G_k:δ)<（（n+1）/（δ+1））,this result directly disproves Shi Ronghua conjecture [1].In addtion to this, we will prove that these graphs have the biggest diameters of the kind. On this we propose a new conjecture as follow:Let G be a connected graph on n vertices, then D（G）≤（（n+1）/（δ+1））,where δ is the minimum degree of G.更多还原