图族圈粘接圈的Merrifield-Simmons指标的最小值

The smallest Merrifield-Simmons index of Q(C_k,C_(s_1),C_(s_2),…,C_(s_k)) graphs

图族Q(Ck,Cs1,Cs2,…,Csk)是由圈Ck的每个顶点vi(i=1,2,…,k)分别粘接圈Csi(i=1,2,…,k)而得到的图。本文通过对图族Q(Ck,Cs1,Cs2,…,Csk)的Merrifield-Simmons指标进行研究,刻画出该图族的Merrifield-Simmons指标取得最小值时的图是Q(Ck,C3,C3,…,C3,Cs1+s2+…+sk-3(k-1))。

Q(Ck,Cs1,Cs2,…,Csk)graphs be from Ck whose every vertex vi(i=1,2,…,k)attached one cycle Csi(i=1,2,…,k).In this paper,we determined the lowest bound for Merrifield-Simmons index in Q(Ck,Cs1,Cs2,…,Csk)graphs.And characterize the Q(Ck,C3,C3,…,C3,Cs1+s2+…+sk-3(k-1)) graph has the smallest Merrifield-Simmons index of those graphs.