Let S_n~(p,q)denote the graph obtained from cycles C_p and C_q by attaching n +1 – p – q pendent edges to the unique common vertex of them. Let P_n~(p,q)be thegraph consisting of two disjoint cycles C_p, andC_qand a path of length n – p–q +1joining them (when n – p – q + 1 = 0, P_n~(p,q)coincides with S_n~(p,q)). In this paper, weshow that among all n-vertex bicyclic graphs with exactly two cycles: (a) P_n~(3,3)hasthe maximal Kirchhoff index, (b) the following graphs have the minimal Kirchhoffindices: S_5~(3,3);S_6~(3,4); 7~(4,4);8~(4,4)and 4,5);S_n~(4,4)(9 < n 11); ,S_(12)~(4,4),3,4)andS_(12)~(3,3);(n > 12).
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