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English version: Journal of Applied and Industrial Mathematics, 2018, 12:4, 642–647 |
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Volume 25, No 4, 2018, P. 5-14 UDC 519.17
Keywords: graph, vertex transmission, transmission irregular graph, Wiener index. DOI: 10.17377/daio.2018.25.620 Andrey A. Dobrynin 1 Received 3 May 2018 References[1] A. Abiad, B. Brimkov, B. Erey, L. Leshock, X. Martinez-Rivera, S. O. S.-Y. Song, and J. Williford, On the Wiener index, distance cospectrality and transmission-regular graphs, Discrete Appl. Math., 230, 1–10,2017. [2] Y. Alizadeh, V. Andova, S. Klavzar, and R. Škrekovski, Wiener dimension: Fundamental properties and (5, 0)-nanotubical fullerenes, MATCH Commun. Math. Comput. Chem., 72, 279–294, 2014. [3] Y. Alizadeh and S. Klavzar, Complexity of topological indices: the case of connective eccentric index, MATCH Commun. Math. Comput. Chem., 76, 659–667, 2016. [4] Y. Alizadeh and S. Klavzar, On graphs whose Wiener complexity equals their order and on Wiener index of asymmetric graphs, Appl. Math. Comput., 328, 113–118, 2018. [5] K. Balakrishnan, B. Brešar, M. Changat, S. Klavzar, M. Kovše, and A. R. Subhamathi, Computing median and antimedian sets in median graphs, Algorithmica, 57, 207–216, 2010. [6] D. Bonchev, Shannon’s information and complexity, in Complexity in Chemistry: Introduction and Fundamentals, pp. 155–187, Taylor & Francis, Lon?don, 2003 (Math. Chem. Ser., Vol. 7). [7] M. Dehmer and F. Emmert-Streib (eds.), Quantitative Graph Theory: Mathematical Foundations and Applications, CRC Press, Boca Raton, 2014 (Discrete Math. Its Appl.). [8] A. A. Dobrynin, R. Entringer, and I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math., 66, No. 3, 211–249, 2001. [9] A. A. Dobrynin, I. Gutman, S. Klavzar, and P. Zigert, Wiener index of hexagonal systems, Acta Appl. Math., 72, No. 3, 247–294, 2002. [10] A. A. Dobrynin and L. S. Mel’nikov, Wiener index of line graphs, in Distance in Molecular Graphs — Theory, pp. 85–121, Univ. Kragujevac, Kragujevac, 2012 (Math. Chem. Monogr., Vol. 12). [11] R. C. Entringer, Distance in graphs: Trees, J. Combin. Math. Combin. Comput., 24, 65–84, 1997. [12] R. C. Entringer, D. E. Jackson, and D. A. Snyder, Distance in graphs, Czechoslov. Math. J., 26, 283–296, 1976. [13] I. Gutman and B. Furtula (eds.), Distance in Molecular Graphs — Theory, Univ. Kragujevac, Kragujevac, 2012 (Math. Chem. Monogr., Vol. 12). [14] I. Gutman and B. Furtula (eds.), Distance in Molecular Graphs — Applications, Univ. Kragujevac, Kragujevac, 2012 (Math. Chem. Monogr., Vol. 13). [15] I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verl., Heidelberg, 1986. [16] M. Knor and R. Škrekovski, Wiener index of line graphs, in Quantitative Graph Theory: Mathematical Foundations and Applications, pp. 279–301, CRC Press, Boca Raton, 2014 (Discrete Math. Its Appl.). [17] M. Knor, R. Škrekovski, and A. Tepeh, Mathematical aspects of Wiener index, Ars Math. Contemp., 11, No. 2, 327–352, 2016. [18] M. Krnc and R. Škrekovski, Centralization of transmission in networks, Discrete Math., 338, 2412–2420, 2015. [19] J. Plesnik, On the sum of all distances in a graph or digraph, J. Graph Theory, 8, 1–21, 1984. [20] C. Smart and P. J. Slater, Center, median, and centroid subgraphs, Networks, 34, 303–311, 1999. [21] N. Trinajstic, Chemical Graph Theory, CRC Press, Boca Raton, 1983. |
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