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General Atom-Bond-Connectivity Index Of Graphs

Yıl 2022, Cilt: 18 Sayı: 1, 91 - 94, 25.03.2022
https://doi.org/10.18466/cbayarfbe.975636

Öz

The Atom-bond-connectivity index ABC of a graph G is determined by d_i and d_j. In this paper, sharp results for the general ABC index which has chemical applications are found using different methods. These new results for ABC inex are investigated in terms of its edges, its vertices and its degrees. In particular, some relations for general ABC index is obtained involving different topological indices; Randic index, Zagreb index, Harmonic index and Narumi-Katayama index. Indeed, general ABC index are improved by the help of the maximum annd minimum degrees.

Kaynakça

  • Ahmadi, M.B., Dimitrov, D., Gutman, I., Hosseini, S.A., Disproving a conjecture on trees with minimal atom-bond connectivity index, MATCH Commun. Math. Comput. Chem. 72, 685-698, 2014.
  • Randi´c, M., On characterization of molecular branching, J. Amer. Chem. Soc. 97, 6609-6615, 1975.
  • Bapat, R.B., Graphs and Matrices, Indian Statistical Institute, New Delhi 110016,India, 2010.
  • Bianchi, M., Cornaro, A., Palacios, J.L., Torriero, A., New upper bounds for the ABC index, MATCH Commun. Math. Comput. Chem. 76, 117-130, 2016.
  • Borovi´canin, B., Furtula, B., On extremal Zagreb indices of trees with given domination number, Appl. Math. Comput. 279, 208-218, 2016.
  • Büyükköse, S., Altınk, E., Yalçın, F., Improved Bounds for the Extremal Non-trivial Laplacian Eigenvalues, Gazi University Journal of Science, 28, (1), 65-68, 2015.
  • Das, K.C., Atom-bond connectivity index of graphs, Discr. Appl. Math. 158, 1181-1188, 2010.
  • Das, K.C., On comparing Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 63, 433-440, 2010.
  • Ghorbani, M., Songhori, M., Gutman, I., Modified Narumi-Katayama index, Kragujevac J. Sci. 34, 5764, 2012.
  • Gutman, I., Degree-based topological indices, Croat. Chem. Acta 86, 351-361, 2013.
  • Jos´e, M.R., Jos´e, M.S., New Results on the Harmonic Index and Its Generalizations, MATCH Commun. Math. Comput. Chem. 78, 387-404, 2017.
  • Fajtlowicz, S., On conjectures of Graffiti-II, Congr. Num. 60, 187-197, 1987.
  • Kaya Gök, G., Some Bounds on the Distance-Sum-Connectivity Matrix, Journal of Inequalities and Applications, 171, 2018.
  • Wua, R., Tanga, Z., Deng, H., A lower bound for the harmonic index of a graph with minimum degree at least two, Filomat 27, 51-55, 2013.
Yıl 2022, Cilt: 18 Sayı: 1, 91 - 94, 25.03.2022
https://doi.org/10.18466/cbayarfbe.975636

Öz

Kaynakça

  • Ahmadi, M.B., Dimitrov, D., Gutman, I., Hosseini, S.A., Disproving a conjecture on trees with minimal atom-bond connectivity index, MATCH Commun. Math. Comput. Chem. 72, 685-698, 2014.
  • Randi´c, M., On characterization of molecular branching, J. Amer. Chem. Soc. 97, 6609-6615, 1975.
  • Bapat, R.B., Graphs and Matrices, Indian Statistical Institute, New Delhi 110016,India, 2010.
  • Bianchi, M., Cornaro, A., Palacios, J.L., Torriero, A., New upper bounds for the ABC index, MATCH Commun. Math. Comput. Chem. 76, 117-130, 2016.
  • Borovi´canin, B., Furtula, B., On extremal Zagreb indices of trees with given domination number, Appl. Math. Comput. 279, 208-218, 2016.
  • Büyükköse, S., Altınk, E., Yalçın, F., Improved Bounds for the Extremal Non-trivial Laplacian Eigenvalues, Gazi University Journal of Science, 28, (1), 65-68, 2015.
  • Das, K.C., Atom-bond connectivity index of graphs, Discr. Appl. Math. 158, 1181-1188, 2010.
  • Das, K.C., On comparing Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 63, 433-440, 2010.
  • Ghorbani, M., Songhori, M., Gutman, I., Modified Narumi-Katayama index, Kragujevac J. Sci. 34, 5764, 2012.
  • Gutman, I., Degree-based topological indices, Croat. Chem. Acta 86, 351-361, 2013.
  • Jos´e, M.R., Jos´e, M.S., New Results on the Harmonic Index and Its Generalizations, MATCH Commun. Math. Comput. Chem. 78, 387-404, 2017.
  • Fajtlowicz, S., On conjectures of Graffiti-II, Congr. Num. 60, 187-197, 1987.
  • Kaya Gök, G., Some Bounds on the Distance-Sum-Connectivity Matrix, Journal of Inequalities and Applications, 171, 2018.
  • Wua, R., Tanga, Z., Deng, H., A lower bound for the harmonic index of a graph with minimum degree at least two, Filomat 27, 51-55, 2013.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Seda Kınacı 0000-0002-5334-5091

Yayımlanma Tarihi 25 Mart 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 18 Sayı: 1

Kaynak Göster

APA Kınacı, S. (2022). General Atom-Bond-Connectivity Index Of Graphs. Celal Bayar University Journal of Science, 18(1), 91-94. https://doi.org/10.18466/cbayarfbe.975636
AMA Kınacı S. General Atom-Bond-Connectivity Index Of Graphs. CBUJOS. Mart 2022;18(1):91-94. doi:10.18466/cbayarfbe.975636
Chicago Kınacı, Seda. “General Atom-Bond-Connectivity Index Of Graphs”. Celal Bayar University Journal of Science 18, sy. 1 (Mart 2022): 91-94. https://doi.org/10.18466/cbayarfbe.975636.
EndNote Kınacı S (01 Mart 2022) General Atom-Bond-Connectivity Index Of Graphs. Celal Bayar University Journal of Science 18 1 91–94.
IEEE S. Kınacı, “General Atom-Bond-Connectivity Index Of Graphs”, CBUJOS, c. 18, sy. 1, ss. 91–94, 2022, doi: 10.18466/cbayarfbe.975636.
ISNAD Kınacı, Seda. “General Atom-Bond-Connectivity Index Of Graphs”. Celal Bayar University Journal of Science 18/1 (Mart 2022), 91-94. https://doi.org/10.18466/cbayarfbe.975636.
JAMA Kınacı S. General Atom-Bond-Connectivity Index Of Graphs. CBUJOS. 2022;18:91–94.
MLA Kınacı, Seda. “General Atom-Bond-Connectivity Index Of Graphs”. Celal Bayar University Journal of Science, c. 18, sy. 1, 2022, ss. 91-94, doi:10.18466/cbayarfbe.975636.
Vancouver Kınacı S. General Atom-Bond-Connectivity Index Of Graphs. CBUJOS. 2022;18(1):91-4.