[1] D. Bauer, H. J. Bro ersma, J. van den Heuvel, N. Kahl, A. Nevo, E. Schmeichel, D. R. Wo o dall and M. Yatauro, Best monotone degree conditions for graph prop erties: a survey, Graphs Combin., 31 (2015) 1-22.
[2] C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1973.
[3] J. A. Bondy, Prop erties of graphs with constraints on degrees, Studia Sci. Math. Hungar., 4 (1969) 473-475.
[4] W. Byer and D. Smeltzer, Edge b ounds in nonhamiltonian k -connected graphs, Discrete Math., 307 (2007) 1572-1579.
[5] L. Chen, J. Liu and Y. Shi, Matching energy of unicyclic and bicyclic graphs with a given diameter, Complexity, 21 (2015) 224-238.
[6] L. Chen and Y. T. Shi, The maximal matching energy of tricyclic graphs, MATCH Commun. Math. Comput. Chem., 73 (2015) 105-120.
[7] Z. Chen, M. Dehmer, Y. Shi and H. Yang, Sharp upp er b ounds for the Balaban index of bicyclic graphs, MATCH Commun. Math. Comput. Chem., 75 (2016) 105-128.
[8] V. Chvatal, On Hamiltons ideals, J. Combin. Theory Ser. B., 12 (1972) 163-168.
[9] A. Dobrynin, R. Entringerand I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math., 66 (2001) 211-249.
[10] S. Gupta, M. Singh and A. K. Madan, Connective eccentricity index: a novel top ological descriptor for predicting biological activity, J. Mol. Graph. Model., 18 (2000) 18{25.
[11] S. Gupta, M. Singh and A. K. Madan, Eccentric distance sum: A novel graph invariant for predicting biological and physical prop erties, J. Math. Anal. Appl., 275 (2002) 386{401.
[12] H. Hua and M. Wang, On Harary index and traceable graphs, MATCH Commun. Math. Comput. Chem., 70 (2013) 297-300.
[13] A. Ilic, G. H. Yu and L. H. Feng, On the eccentric distance sum of graphs, J. Math. Anal. Appl., 381 (2011) 590-600.
[14] O. Ivanciuc, QSAR comparative study of Wiener descriptors for weighted molecular graphs, J. Chem. Inf. Comput. Sci., 40 (2000) 1412-1422.
[15] R. Li, Harary index and some Hamiltonian prop erties of graphs, AKCE Inter. J. of Graphs and Comb., 12 (2015) 64-69.
[16] R. Li, Wiener index and some Hamiltonian prop erties of graphs, Inter. J. of Math. and Soft Computing, 5 (2015) 11-16.
[17] S. Li and Y. Song, On the sum of all distances in bipartite graphs, Discrete Appl. Math., 169 (2014) 176-185.
[18] S. C. Li, M. Zhang, G. H. Yu and L. H. Feng, On the extremal values of the eccentric distance sum of trees, J. Math. Anal. Appl., 390 (2012) 99-112.
[19] J. Ma, Y. Shi, Z. Wang and J. Yue, On Wiener p olarity index of bicyclic networks, Sci. Rep., 6 (2016) 19066. doi:10.1038/srep19066.
[20] J. Ma, Y.bT. Shi and Y. Yue, The Wiener p olarity index of graph pro ducts, Ars Combin., 116 (2014) 235{244.
[21] J. Plesnk, On the sum of all distances in a graph or diagraph, J. Graph Theory, 8 (1984) 1-21.
[22] V. Sharma, R. Goswami, A. K. Madan, Eccentric connectivity index: A novel highly discriminating top ological descriptor for structure prop erty and structure activity studies, J. Chem. Inf. Comput. Sci., 37 (1997) 273-282.
[23] S. Sardana, A. K. Madan, Predicting anti-HIV activity of TIBO derivatives: A computational approach using a novel top ological descriptor, J. Mol. Model., 8 (2002) 258-265.
[24] Y. Shi, Note on two generalizations of the Randic index, Appl. Math. Comput., 265 (2015) 1019-1025.
[25] L. Yang, Wiener index and traceable graphs, Bul l. Austral. Math. Soc., 88 (2013) 380-383.
[26] G.H. Yu, L.H. Feng, A. Ilic, On the eccentric distance sum of trees and unicyclic graphs, J. Math. Anal. Appl., 375 (2011) 99-07.
[27] G.H. Yu, H. Qu, L. Tang, L.H. Feng, On the connective eccentricity index of trees and unicyclic graphs with given diameter, J. Math. Aanl. Appl., 420 (2014) 1776-1786.
[28] B. Zhou, Z. Du, On eccentric connectivity index, MATCH Commun. Math. Comput. Chem., 63 (2010) 181-198.