On minimum revised edge Szeged index of bicyclic graphs

References

• Aouchiche, M, Hansen, P. (2010). On a conjecture about the Szeged index. Eur. J. Combin. 31(7): 1662–1666.
   Google Scholar
• Azari, M. (2017). Some variants of the Szeged index under rooted product of graphs. MMN 17(2): 761–775.
   Google Scholar
• Bonamy, M., Knor, M., Lužar, B., Pinlou, A, Škrekovski, R. (2017). On the difference between the Szeged and Wiener index. Appl. Math. Comput. 312: 202–213.
   Google Scholar
• Bondy, J. A, Murty, U. S. R. (2008). Graph Theory. Berlin: Springer-Verlag.
   Google Scholar
• Cai, X, Zhou, B. (2010). Edge Szeged index of Unicyclic graphs. MATCH Commun. Math. Comput. Chem. 63: 133–144.
   Web of Science ®Google Scholar
• Chen, L., Li, X, Liu, M. (2014). The (revised) Szeged index and the Wiener index of a nonbipartite graph. Euro. J. Comb. 36: 237–246.
   Web of Science ®Google Scholar
• Chen, L., Li, X, Liu, M. (2014). Tricyclic graphs with maximal revised Szeged index. Discr. Appl. Math. 177: 71–79.
   Google Scholar
• Chen, L., Li, X., Liu, M, Gutman, I. (2012). On a relation between the Szeged index and the Wiener index for bipartite graphs. Trans. Comb. 1(4): 43–49.
   Google Scholar
• Črepnjak, M, Tratnik, N. (2017). The Szeged index and the Wiener index of partial cubes with applications to chemical graphs. Appl. Math. Comput. 309: 324–333.
   Web of Science ®Google Scholar
• Dobrynin, A. A., Entringer, R, Gutman, I. (2001). Wiener index of trees: theory and applications. Acta Appl. Math. 66(3): 211–249.
   Web of Science ®Google Scholar
• Dong, H., Zhou, B, Trinajstić, C. (2011). A novel version of the edge-Szeged index. Croat. Chem. Acta 84: 543–545.
   Google Scholar
• Gutman, I. (1994). A formula for the Wiener number of trees and its extension to graphs containing cycles. Graph Theory Notes N. Y. 27: 9–15.
   Google Scholar
• Gutman, I, Ashrafi, A. R. (2008). The edge version of the Szeged index. Croat. Chem. Acta 81: 263–266.
   Web of Science ®Google Scholar
• Gutman, I., Klavžar, S, Mohar, B. (1997). Fifty years of the Wiener index. MATCH Commun. Math. Comput. Chem 35: 1–259.
   Google Scholar
• Gutman, I., Yeh, Y. N., Lee, S. L, Luo, Y. L. (1993). Some recent results in the theory of the Wiener number. Indian J. Chem. 32A: 651–661.
   Google Scholar
• Khalifeh, M. H., Yousefi-Azari, H., Ashrafi, A. R, Gutman, I. (2008). The edge Szeged index of product graphs. Croat. Chem. Acta 81: 277–281.
   Web of Science ®Google Scholar
• Khadikar, P., Kale, P., Deshpande, N., Karmarkar, S, Agrawal, V. (2000). Szeged indices of hexagonal chains. MATCH Commun. Math. Comput. Chem. 43: 7–15.
   Google Scholar
• Khadikar, P., Karmarkar, S., Agrawal, V. K., Singh, J., Shrivastava, A., Lukovits, I, Diudea, M. V. (2005). Szeged index-Applications for drug modeling. LDDD 2(8): 606–624.
   Google Scholar
• Li, S, Zhang, H. (2017). Proofs of three conjectures on the quotients of the (revised) Szeged index and the Wiener index and beyond. Discr. Math. 340(3): 311–324.
   Web of Science ®Google Scholar
• Li, X, Liu, M. (2013). Bicyclic graphs with maximal revised Szeged index. Discr. Appl. Math. 161(16–17): 2527–2531.
   Google Scholar
• Liu, M, Chen, L. (2016). Bicyclic graphs with maximal edge revised Szeged index. Discr. Appl. Math. 215: 225–230.
   Google Scholar
• Nadjafi-Arani, M. J., Khodashenas, H, Ashrafi, A. R. (2011). On the differences between Szeged and Wiener indices of graphs. Discr. Math. 311(20): 2233–2237.
   Google Scholar
• Nadjafi-Arani, M. J., Khodashenas, H, Ashrafi, A. R. (2012). Graphs whose Szeged and Wiener numbers differ by 4 and 5. Math. Comput. Model. 55(3–4): 1644–1648.
   Google Scholar
• Pisanski, T, Randić, M. (2010). Use of the Szeged index and the revised Szeged index for measuring network bipartivity. Discr. Appl. Math. 158(17): 1936–1944.
   Web of Science ®Google Scholar
• Randić, M. (2002). On generalization of Wiener index for cyclic structures. Acta Chim. Slov. 49: 483–496.
   Web of Science ®Google Scholar
• Simić, S., Gutman, I, Baltić, V. (2000). Some graphs with extremal Szeged index. Math. Slovaca 50: 1–15.
   Google Scholar
• Tratnik, N. (2017). The edge-Szeged index and the PI index of benzenoid systems in linear time. MATCH Commun. Math. Comput. Chem. 77: 393–406.
   Web of Science ®Google Scholar
• Vukičević, D. (2009). Note on the graphs with the greatest edge-Szeged index. MATCH Commun. Math. Comput. Chem. 61: 673–681.
   Google Scholar
• Wang, S. (2017). On extremal cacti with respect to the Szeged index. Appl. Math. Comput. 309: 85–92.
   Google Scholar
• Wiener, H. (1947). Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69(1): 17–20.
   PubMed Web of Science ®Google Scholar
• Xing, R, Zhou, B. (2011). On the revised Szeged index. Discr. Appl. Math. 159(1): 69–78.
   Google Scholar
• Žerovnik, J. (1999). Szeged index of symmetric graphs. J. Chem. Inf. Comput. Sci. 39(1): 77–80.
   Google Scholar
• Zhang, H., Chen, J, Li, S. (2017). On the quotients between the (revised) Szeged index and Wiener index of graphs. Discr. Math. Theor. Comput. Sci. 19(1): 12–25.
   Google Scholar
• Zhang, H., Li, S, Zhao, L. (2016). On the further relation between the (revised) Szeged index and Wiener index. Discr. Appl. Math. 206: 152–164.
   Google Scholar