Abstract
The solution of Königsberg Bridge Problem in 1736 by a great Swiss mathematician Leonhard Euler (1707–1783) gave birth to a novel subject—Graph Theory, which also made him the father of graph theory.
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References
Bondy JA, Murty USR (1976) Graph theory with applications. Macmillan Press, New York
Harary F (1969) Graph theory. Addison-Wesley, Reading
Brouwer AE, Cohen AM, Neumaier A (1989) Distance-regular graphs. Springer, Berlin
Biggs NL (1993) Distance-transitive graphs. Algebraic graph theory, 2nd edn. Cambridge University Press, Cambridge
Buckley F, Harary F (1990) Distance in graphs. Addison-Wesley, Redwood
Goddard W, Oellermann OR (2011) Structural analysis of complex networks. Distance in graphs. Birkhäuser/Springer, New York, pp 49–72
Janežič D, Miličević A, Nikolić S, Trinajstić N (2007) Graph theoretical matrices in chemistry. University of Kragujevac, Kragujevac
Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley-VCH, Weinheim, pp 497–502
Todeschini R, Consonni V (2009) Molecular descriptors for chemoinformatics, vol I, vol II. Wiley-VCH, Weinheim, pp 934–938
Gutman I, Furtula B (eds) (2012) Distance in molecular graphs-theory. University of Kragujevac, Kragujevac
Gutman I, Furtula B (eds) (2012) Distance in molecular graphs-applications. University of Kragujevac, Kragujevac
Trinajstić N (1992) Chemical graph theory. CRC Press, Boca Raton
Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69:17–20
Hosoya H (1971) Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull Chem Soc Jpn 44:2332–2339
Randić M (1993) Novel molecular descriptor for structure-property studies. Chem Phys Lett 211:478–483
Klein DJ, Lukovits I, Gutman I (1995) On the definition of the hyper-Wiener index for cycle-containing structures. J Chem Inf Comput Sci 35:50–52
Plavšić D, Nikolić S, Trinajstić N, Mihalić Z (1993) On the Harary index for the characterization of chemical graphs. J Math Chem 12:235–250
Ivanciuc O, Balaban TS, Balaban AT (1993) Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices. J Math Chem 12:309–318
Mihalić Z, Trinajstić N (1992) A graph-theoretical approach to structure-property relationships. J Chem Educ 69:701–712
Xu K, Das KC (2011) On Harary index of graphs. Discret Appl Math 159:1631–1640
Zhou B, Du Z, Trinajstić N (2008) Harary index of landscape graphs. Int J Chem Model 1:35–44
Ivanciuc O (2000) QSAR comparative study of Wiener descriptors for weighted molecular graphs. J Chem Inf Comput Sci 40:1412–1422
Ivanciuc O, Ivanciuc T, Balaban AT (2000) The complementary distance matrix, a new molecular graph metric. ACH Models Chem 137:57–82
Gutman I, Furtula B, Petrović M (2009) Terminal Wiener index. J Math Chem 46:522–531
Székely LA, Wang H, Wu T (2011) The sum of distances between the leaves of a tree and the semi-regular property. Discret Math 311:1197–1203
Gutman I (1994) A formula for the Wiener number of trees and its extension to graphs containing cycles. Graph Theory Notes NY 27:9–15
Balaban AT (1982) Highly discriminating distance based topological index. Chem Phys Lett 89:399–404
Balaban AT (1983) Topological indices based on topological distances in molecular graphs. Pure Appl Chem 55:199–206
Dobrynin AA, Entringer R, Gutman I (2001) Wiener index of trees: theory and applications. Acta Appl Math 66:211–249
Dobrynin AA, Gutman I, Klavžar S, Žiget P (2002) Wiener index of hexagonal systems. Acta Appl Math 72:247–294
Feng L, Ilić A (2010) Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number. Appl Math Lett 23:943–948
Furtula B, Gutman I, Tomović Ž, Vesel A, Pesek I (2002) Wiener-type topological indices of phenylenes. Indian J Chem A 41:1767–1772
Gutman I (1997) A property of the Wiener number and its modifications. Indian J Chem A 36:128–132
Gutman I, Rada J, Araujo O (2000) The Wiener index of starlike trees and a related partial order. MATCH Commun Math Comput Chem 42:145–154
Liu M, Liu B (2010) Trees with the seven smallest and fifteen greatest hyper-Wiener indices. MATCH Commun Math Comput Chem 63:151–170
Nikolić S, Trinajstić N, Mihalić Z (1995) The Wiener index: development and applications. Croat Chem Acta 68:105–129
Zhou B, Trinajstić N (2010) Mathematical properties of molecular descriptors based on distances. Croat Chem Acta 83:227–242
Bonchev D, Trinajstić N (1977) Information theory, distance matrix, and molecular branching. J Chem Phys 67:4517–4533
Mohar B, Babić D, Trinajstić N (1993) A novel definition of the Wiener index for trees. J Chem Inf Comput Sci 33:153–154
Gutman I (1994) Selected properties of the Schultz molecular topogical index. J Chem Inf Comput Sci 34:1087–1089
Nikolić S, Trinajstić N, Randić M (2001) Wiener index revisited. Chem Phys Lett 333:319–321
Zhou B (2010) Reverse Wiener index. In: Gutman I, Furtula B (eds) Novel molecular structure descriptors-theory and applications II. University of Kragujevac, Kragujevac, pp 193–204
Ghorbani M (2012) Computing Wiener index of chemical compounds by cut method. In: Gutman I, Furtula B (eds) Distance in molecular graphs-theory. University of Kragujevac, Kragujevac, pp 71–83
Ghorbani M, Ashrafi AR, Zousefi S (2012) Wiener index of nanotubes and nanotori. In: Gutman I, Furtula B (eds) Distance in molecular graphs-application. University of Kragujevac, Kragujevac, pp 157–166
Balaban TS, Filip PA, Ivanciuc O (1992) Computer generation of acyclic graphs based on local vertex invariants and topological indices. Derived canonical labelling and coding trees and alkanes. J Math Chem 11:79–105
Lučić B, Sović I, Plavšić D, Trinajstić N (2012) Harary matrices: definitions, properties and applications. In: Gutman I, Furtula B (eds) Distance in molecular graphs-applications. University of Kragujevac, Kragujevac, pp 3–26
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Xu, K., Das, K.C., Trinajstić, N. (2015). Introduction. In: The Harary Index of a Graph. SpringerBriefs in Applied Sciences and Technology(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45843-3_1
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