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Degree distance and Gutman index of two graph products

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

Abstract

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.

References

  • [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.
Year 2020, , 121 - 140, 07.05.2020
https://doi.org/10.13069/jacodesmath.729422

Abstract

References

  • [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.
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Shaban Sedghı This is me

Nabi Shobe This is me

Publication Date May 7, 2020
Published in Issue Year 2020

Cite

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. May 2020;7(2):121-140. doi:10.13069/jacodesmath.729422
Chicago Sedghı, Shaban, and Nabi Shobe. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications 7, no. 2 (May 2020): 121-40. https://doi.org/10.13069/jacodesmath.729422.
EndNote Sedghı S, Shobe N (May 1, 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 and N. Shobe, “Degree distance and Gutman index of two graph products”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 7, no. 2, pp. 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 (May 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 and Nabi Shobe. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 7, no. 2, 2020, pp. 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

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https://doi.org/10.13069/jacodesmath.935980