Erratum to: Tutte polynomials for benzenoid systems with one branched hexagon

1 Erratum to: J Math Chem (2016) 54:1057–1071 DOI 10.1007/s10910-016-0601-3

The original version of this article unfortunately contained a mistake. The presentation of Fig. 7 and Eqs. 5, 6 was incorrect in the original publication of the article.

Fig. 7

Expanding the first item in the last identity displayed in Fig. 6

• 1. Although the approach and numerical results in Appendices 1 and 2 are all correct, two errors in Fig. 7 (two revised coefficients are x and 2) were found by Ms. Xiaoying Wu. The correct version of Fig. 7 is given below.

• 2. Accordingly, there were errors in equations following Fig. 7.

  • (a) Page 1062, in the right-hand side of Eq. (5),

    $$\begin{aligned} 4T_l ^{{\prime }}T_m ^{{\prime }}T_n ^{{\prime }}\hbox { should be }\left( {x+2} \right) T_l ^{{\prime }}T_m ^{{\prime }}T_n ^{{\prime }}. \end{aligned}$$

  • (b) Page 1063, in the right-hand side of Eq. (6);

    Page 1064, in the recurrences before Theorem 3.1;

    Page 1065, in the second formula of Theorem 3.1:

    $$\begin{aligned} \hbox {all }\left( {y^{2}+y+5} \right) \hbox {'s should be }\left( {y^{2}+y+x+3} \right) \hbox {'s}, \end{aligned}$$

  • c. In both the right-hand side of Eq. (6) and the second formula of Theorem 3.1:

    $$\begin{aligned}&-4y^{4}\hbox { should be }-(x+2)y^{4},\\&\frac{4y^{9}-3y^{8}-y^{4}}{y-1}\hbox { should be } \frac{(x+2)y^{9}-(x+1)y^{8}-y^{4}}{y-1},\\&\frac{-4y^{13}+2y^{12}+3y^{8}-y^{3}}{y-1}\hbox { should be } \frac{-(x+2)y^{13}+xy^{12}+3y^{8}-y^{3}}{y-1}. \end{aligned}$$