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Degree distance and Gutman index of two graph products

Yıl 2020, , 121 - 140, 07.05.2020
https://doi.org/10.13069/jacodesmath.729422

Öz

The degree distance was introduced by Dobrynin, Kochetova and
Gutman as a weighted version of the Wiener index. In this paper,
we investigate the degree distance and Gutman index of complete,
and strong product graphs by using the adjacency and
distance matrices of a graph.

Kaynakça

  • [1] A. Alwardi, B. Arsic, I. Gutman, N. D. Soner, The common neighborhood graph and its energy, Iran. J. Math. Sci. Inf. 7 (2012) 1–8.
  • [2] J. A. Bondy, U. S. R. Murty, Graph theory, Springer, New York, 2008.
  • [3] A. S. Bonifácio, R. R. Rosa, I. Gutman, N. M. M. de Abreu, Complete common neighborhood graphs, Proceedings of Congreso Latino-Iberoamericano de Investigaci on Operativa and Simposio Brasileiro de Pesquisa Operacional (2012) 4026–4032.
  • [4] S. Chen, Cacti with the smallest, second smallest, and third smallest Gutman index, J. Combin. Optim. 31(1) (2016) 327–332.
  • [5] S. Chen, Z. Guo, A lower bound on the degree distance in a tree, Int. J. Contemp. Math. Sci. 5(13) (2010) 649–652.
  • [6] P. Dankelmann, I. Gutman, S. Mukwembi, H.C. Swart, On the degree distance of a graph, Discrete Appl. Math. 157(13) (2009) 2773–2777.
  • [7] P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, The edge–Wiener index of a graph, Discrete Math. 309 (2009) 3452–457.
  • [8] A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math. 66 (2001) 211–249.
  • [9] A. A. Dobrynin, A. A. Kochetova, Degree distance of a graph: A degree analogue of the Wiener index, J. Chem. Inf. Comput. Sci. 34(5) (1994) 1082–1086.
  • [10] T. Došlic, B. Furtula, A. Graovac, I. Gutman, S. Moradi, Z. Yarahmadi, On vertex–degree–based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66 (2011) 613–626.
  • [11] A. A. Dobrynin, I. Gutman, S. Klavžar, P. Žigert, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002) 247–294.
  • [12] L. Feng, W. Liu, The maximal Gutman index of bicyclic graphs, MATCH Commun. Math. Comput. Chem. 66 (2011) 699–708.
  • [13] I. Gutman, Y. N. Yeh, S. L. Lee, Y. L. Luo, Some recent results in the theory of the Wiener number, Indian J. Chem. 32A (1993) 651–661.
  • [14] I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34(5) (1994) 1087–1089.
  • [15] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17(4) (1972) 535–538.
  • [16] P. Paulraja, V.S. Agnes, Degree distance of product graphs, Discrete Math., Alg. and Appl. 6(1) (2014) 1450003.
  • [17] P. Paulraja, V. S. Agnes, Gutman index of product graphs, Discrete Math., Alg. and Appl. 6(4) (2014) 1450058.
  • [18] R. Hammack, W. Imrich, Sandi Klav˘zr, Handbook of product graphs, Second edition, CRC Press, 2011.
  • [19] S. Nikolic, N. Trinajstic, Z. Mihalic, The Wiener index: Development and applications, Croat. Chem. Acta 68 (1995) 105–129.
  • [20] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.
  • [21] H.P. Schultz, Topological organic chemistry. 1. Graph theory and topological indices of alkanes, J. Chem. Inf. Comput. Sci. 29(3) (1989) 227–228.
Yıl 2020, , 121 - 140, 07.05.2020
https://doi.org/10.13069/jacodesmath.729422

Öz

Kaynakça

  • [1] A. Alwardi, B. Arsic, I. Gutman, N. D. Soner, The common neighborhood graph and its energy, Iran. J. Math. Sci. Inf. 7 (2012) 1–8.
  • [2] J. A. Bondy, U. S. R. Murty, Graph theory, Springer, New York, 2008.
  • [3] A. S. Bonifácio, R. R. Rosa, I. Gutman, N. M. M. de Abreu, Complete common neighborhood graphs, Proceedings of Congreso Latino-Iberoamericano de Investigaci on Operativa and Simposio Brasileiro de Pesquisa Operacional (2012) 4026–4032.
  • [4] S. Chen, Cacti with the smallest, second smallest, and third smallest Gutman index, J. Combin. Optim. 31(1) (2016) 327–332.
  • [5] S. Chen, Z. Guo, A lower bound on the degree distance in a tree, Int. J. Contemp. Math. Sci. 5(13) (2010) 649–652.
  • [6] P. Dankelmann, I. Gutman, S. Mukwembi, H.C. Swart, On the degree distance of a graph, Discrete Appl. Math. 157(13) (2009) 2773–2777.
  • [7] P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, The edge–Wiener index of a graph, Discrete Math. 309 (2009) 3452–457.
  • [8] A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math. 66 (2001) 211–249.
  • [9] A. A. Dobrynin, A. A. Kochetova, Degree distance of a graph: A degree analogue of the Wiener index, J. Chem. Inf. Comput. Sci. 34(5) (1994) 1082–1086.
  • [10] T. Došlic, B. Furtula, A. Graovac, I. Gutman, S. Moradi, Z. Yarahmadi, On vertex–degree–based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66 (2011) 613–626.
  • [11] A. A. Dobrynin, I. Gutman, S. Klavžar, P. Žigert, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002) 247–294.
  • [12] L. Feng, W. Liu, The maximal Gutman index of bicyclic graphs, MATCH Commun. Math. Comput. Chem. 66 (2011) 699–708.
  • [13] I. Gutman, Y. N. Yeh, S. L. Lee, Y. L. Luo, Some recent results in the theory of the Wiener number, Indian J. Chem. 32A (1993) 651–661.
  • [14] I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34(5) (1994) 1087–1089.
  • [15] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17(4) (1972) 535–538.
  • [16] P. Paulraja, V.S. Agnes, Degree distance of product graphs, Discrete Math., Alg. and Appl. 6(1) (2014) 1450003.
  • [17] P. Paulraja, V. S. Agnes, Gutman index of product graphs, Discrete Math., Alg. and Appl. 6(4) (2014) 1450058.
  • [18] R. Hammack, W. Imrich, Sandi Klav˘zr, Handbook of product graphs, Second edition, CRC Press, 2011.
  • [19] S. Nikolic, N. Trinajstic, Z. Mihalic, The Wiener index: Development and applications, Croat. Chem. Acta 68 (1995) 105–129.
  • [20] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.
  • [21] H.P. Schultz, Topological organic chemistry. 1. Graph theory and topological indices of alkanes, J. Chem. Inf. Comput. Sci. 29(3) (1989) 227–228.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Shaban Sedghı Bu kişi benim

Nabi Shobe Bu kişi benim

Yayımlanma Tarihi 7 Mayıs 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Sedghı, S., & Shobe, N. (2020). Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications, 7(2), 121-140. https://doi.org/10.13069/jacodesmath.729422
AMA Sedghı S, Shobe N. Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications. Mayıs 2020;7(2):121-140. doi:10.13069/jacodesmath.729422
Chicago Sedghı, Shaban, ve Nabi Shobe. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications 7, sy. 2 (Mayıs 2020): 121-40. https://doi.org/10.13069/jacodesmath.729422.
EndNote Sedghı S, Shobe N (01 Mayıs 2020) Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications 7 2 121–140.
IEEE S. Sedghı ve N. Shobe, “Degree distance and Gutman index of two graph products”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy. 2, ss. 121–140, 2020, doi: 10.13069/jacodesmath.729422.
ISNAD Sedghı, Shaban - Shobe, Nabi. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications 7/2 (Mayıs 2020), 121-140. https://doi.org/10.13069/jacodesmath.729422.
JAMA Sedghı S, Shobe N. Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7:121–140.
MLA Sedghı, Shaban ve Nabi Shobe. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy. 2, 2020, ss. 121-40, doi:10.13069/jacodesmath.729422.
Vancouver Sedghı S, Shobe N. Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7(2):121-40.

Cited By

General degree distance of graphs
Journal of Algebra Combinatorics Discrete Structures and Applications
Tomáš VETRÍK
https://doi.org/10.13069/jacodesmath.935980