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2015 | 35 | 1 | 17-33
Tytuł artykułu

Harary Index of Product Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula for the Harary index of the wreath product G ○ G′ is obtained.
Słowa kluczowe
Wydawca
Rocznik
Tom
35
Numer
1
Strony
17-33
Opis fizyczny
Daty
wydano
2015-02-01
otrzymano
2013-03-04
poprawiono
2013-10-14
zaakceptowano
2013-12-24
online
2015-02-06
Twórcy
  • Department of Mathematics Annamalai University Annamalainagar 608 002, India, pramank@gmail.com
autor
  • Department of Mathematics Annamalai University Annamalainagar 608 002, India, ppraja56@gmail.com
Bibliografia
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  • [4] B. Breˇsar, W. Imrich, S. Klavˇzar and B. Zmazek, Hypercubes as direct products, SIAM J. Discrete Math. 18 (2005) 778-786. doi:10.1137/S0895480103438358[Crossref]
  • [5] K.C. Das, B. Zhou and N. Trinajsti´c, Bounds on Harary index , J. Math. Chem. 46 (2009) 1377-1393. doi:10.1007/s10910-009-9522-8[Crossref]
  • [6] J. Devillers and A.T. Balaban, (Eds), Topological Indices and Related Descriptors in QSAR and QSPR (Gordon and Breach, Amsterdam, 1999).
  • [7] M.V. Diudea, Indices of reciprocal properties or Harary indices, J. Chem. Inf. Com- put. Sci. 37 (1997) 292-299. doi:10.1021/ci960037w[Crossref]
  • [8] L. Feng and A. Ili´c, Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number , Appl. Math. Lett. 23 (2010) 943-948. doi:10.1016/j.aml.2010.04.017[WoS][Crossref]
  • [9] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer-Verlag, Berlin, 1986). doi:10.1007/978-3-642-70982-1[Crossref]
  • [10] I. Gutman, A property of the Wiener number and its modifications, Indian J. Chem. 36A (1997) 128-132.
  • [11] R. Hammack, W. Imrich and S. Klavˇzar, Handbook of Product Graphs (CRC Press, New York, 2011).
  • [12] M. Hoji, Z. Luo and E. Vumar, Wiener and vertex PI indices of Kronecker products of graphs, Discrete Appl. Math. 158 (2010) 1848-1855. doi:10.1016/j.dam.2010.06.009[Crossref][WoS]
  • [13] O. Ivanciu´c, T.S. Balaban and A.T. Balaban, Reciprocal distance matrix, related local vertex invariants and topological indices, J. Math. Chem. 12 (1993) 309-318. doi:10.1007/BF01164642[Crossref]
  • [14] M.H. Khalifeh, H. Youseri-Azari and A.R. Ashrafi, Vertex and edge PI indices of Cartesian product of graphs, Discrete Appl. Math. 156 (2008) 1780-1789. doi:10.1016/j.dam.2007.08.041[WoS][Crossref]
  • [15] B. Luˇci´c, A. Miliˇcevi´c, S. Nikoli´c and N. Trinajsti´c, Harary index-twelve years later , Croat. Chem. Acta 75 (2002) 847-868.
  • [16] I. Lukovits, Wiener-type graph invariants, in: M.V. Diudea (Ed.), QSPR/QSAR Studies by Molecular Descriptors (Nova Science Publishers, Huntington, New York, 2001).
  • [17] A. Mamut and E. Vumar, Vertex vulnerability parameters of Kronecker products of complete graphs, Inform. Process. Lett. 106 (2008) 258-262. doi:10.1016/j.ipl.2007.12.002[WoS][Crossref]
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  • [19] K. Pattabiraman and P. Paulraja, On some topological indices of the tensor product of graphs, Discrete Appl. Math. 160 (2012) 267-279. doi:10.1016/j.dam.2011.10.020[Crossref]
  • [20] K. Pattabiraman and P. Paulraja, Wiener and vertex PI indices of the strong product of graphs, Discuss. Math. Graph Theory 32 (2012) 749-769. doi:10.7151/dmgt.1647[Crossref]
  • [21] K. Pattabiraman and P. Paulraja, Wiener index of the tensor product of a path and a cycle, Discuss. Math. Graph Theory 31 (2011) 737-751. doi:10.7151/dmgt.1576[Crossref]
  • [22] D. Plavsi´c, S. Nikoli´c, N. Trinajsti´c and Z. Mihali´c, On the Harary index for the characterization of chemical graphs, J. Math. Chem. 12 (1993) 235-250.[Crossref]
  • [23] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors (Wiley-VCH, Weinheim, 2000).
  • [24] N. Trinajsti´c, S. Nikoli´c, S.C. Basak and I. Lukovits, Distance indices and their hyper-counterparts: Intercorrelation and use in the structure-property modeling, SAR and QSAR in Environmental Research 12 (2001) 31-54. doi:10.1080/10629360108035370[Crossref]
  • [25] K. Xu and K.C. Das, On Harary index of graphs, Discrete. Appl. Math. 159 (2011) 1631-1640. doi:10.1016/j.dam.2011.06.003[Crossref]
  • [26] H. Yousefi-Azari, M.H. Khalifeh and A.R. Ashrafi, Calculating the edge Wiener and edge Szeged indices of graphs, J. Comput. Appl. Math. 235 (2011) 4866-4870. doi:10.1016/j.cam.2011.02.019 [WoS][Crossref]
  • [27] B. Zhou, Z.Du and N. Trinajsti´c, Harary index of landscape graphs, Int. J. Chem. Model. 1 (2008) 35-44.
  • [28] B. Zhou, X. Cai and N. Trinajsti´c, On the Harary index , J. Math. Chem. 44 (2008) 611-618. doi:10.1007/s10910-007-9339-2 [Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1777
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