Cycles, the Degree Distance, and the Wiener Index

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References

[1] H. Wiener, “Structural Determination of Paraffin Boiling Points,” Journal of the American Chemical Society, Vol. 69, No. 1, 1947, pp. 17-20. doi:10.1021/ja01193a005

[2] A. A. Dobrynin and A. A. Kochetova, “Degree Distance of A Graph: A Degree Analogue of the Wiener Index,” Journal of Chemical Information and Computer Sciences, Vol. 34, No. 5, 1994, pp. 1082-1086.
doi:10.1021/ci00021a008

[3] P. Dankelmann, I. Gutman, S. Mukwembi and H. C. Swart, “On the Degree Distance of a Graph,” Discrete Applied Mathematics, Vol. 157, No. 13, 2009, pp. 2773-2777.
doi:10.1016/j.dam.2009.04.006

[4] A. A. Dobrynin, R. Entringer and I. Gutman, “Wiener Index of Trees: Theory and Applications,” Acta Applicandae Mathematicae, Vol. 66, No. 3, 2001, pp. 211-249.
doi:10.1023/A:1010767517079

[5] Z. Du and B. Zhou, “Minimum Wiener Indices of Trees and Unicyclic Graphs of Given Matching Number,” Match, Vol. 63, No. 1, 2010, pp. 101-112.

[6] M. Fischermann, A. Hoffmann, D. Rautenbach, L. A. Székely and L. Volkmann, “Wiener Index versus Maximum Degree in Trees,” Discrete Applied Mathematics, Vol. 122, No. 1-3, 2002, pp. 127-137.
doi:10.1016/S0166-218X(01)00357-2

[7] H. Liu and M. Lu, “A Unified Approach to Cacti for Different Indices,” Match, Vol. 58, No. 1, 2007, pp. 183-194.

[8] A. I. Tomescu, “Properties of Connected Graphs Having Minimum Degree Distance,” Discrete Applied Mathematics, Vol. 309, No. 9, 2009, pp. 2745-2748.
doi:10.1016/j.disc.2008.06.031

[9] A. I. Tomescu, “Unicyclic and Bicyclic Graphs Having Minimum Degree Distance,” Discrete Applied Mathematics, Vol. 156, No. 2, 2008, pp. 125-130.
doi:10.1016/j.dam.2007.09.010

[10] I. Gutman, “Selected Properties of the Schultz Molecular Topological Index,” Journal of Chemical Information and Computer Sciences, Vol. 34, No. 5, 1994, pp. 1087-1089.
doi:10.1021/ci00021a009

[11] D. J. Klein, Z. Mihalic′, D. Plav?ic′ and N. Trinajstic′, “Molecular Topological Index: A Relation with the Wiener Index,” Journal of Chemical Information and Computer Sciences, Vol. 32, No. 4, 1992, pp. 304-305.