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Let $C_n$ denote the cycle of order $n$ and $P^{6,6}_n$ the graph obtained from joining two cycles $C_6$ by a path $P_{n-12}$ with its two leaves. Let $\\mathscr{B}_n$ denote the class of all bipartite bicyclic graphs but not the graph $R_{a,b}$, which is obtained from joining two cycles $C_a$ and $C_b$ ($a, b\\geq 10$ and $a \\equiv b\\equiv 2\\, (\\,\\textmd{mod}\\, 4)$) by an edge. In [I. Gutman, D. 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