Araştırma Makalesi
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Zagreb Energy of Weighted Graphs

Yıl 2021, Cilt: 13 Sayı: 1, 162 - 173, 30.06.2021

Öz

In this paper, first Zagreb and second Zagreb matrices are defined for
weighted graphs and accordingly the first Zagreb and second Zagreb energy of
weighted graphs are introduced. Moreover, some upper and lower bounds are
presented for Zagreb energy of positive definite matrix weighted graphs.
Also some bounds are obtained for number weighted and unweighted graphs.

Proje Numarası

21002

Kaynakça

  • [1] Büyükköse, Ş., Mutlu, N., Some bounds for the weighted energy, Sinop Uni. J. Nat. Sci., 1(2016), 62-65.
  • [2] Büyükköse, Ş., Mutlu, N., Nurkahlı S.B., Some bounds for the largest eigenvalue of weighted distance matrix and weighted distance energy, Journal of Science and Arts, 2(2017), 245-256.
  • [3] Consonni, V., Todeschini, R., New spectral index for molecule description, MATCH Communications in Mathematical and in Computer Chemistry, 60(2008), 3-14.
  • [4] Gutman, I., Trinajsti´c, N., Graph theory and molecular orbitals. Total -electron energy of alternant hydrocarbons, Chem. Phys. Lett.,17(1972), 535-538.
  • [5] Gutman, I., Ruscic, B., Trinajstic, N., Wilcox, C.F., Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62(1975), 3399-3405.
  • [6] Gutman, I., The energy of a graph. Berlin Mathmatics-Statistics Forschungszentrum, 103(1978), 1-22.
  • [7] Gutman, I., Polansky, O.E., Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
  • [8] He, C., Wang, W., Li, Y., Liu, L., Some Nordhaus-Gaddum type results of A$\alpha $ -eigenvalues of weighted graphs, Applied Mathematics and Computation, 393(2021), 1-10.
  • [9] Li, X., Shi, Y., Gutman, I., Graph Energy, Springer, New York, 2012.
  • [10] Li, X., Zhao, H., Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem., 50(2004), 57-62.
  • [11] Li, X., Zheng, J., A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem., 54(2005), 195-208.
  • [12] Ozeki, N., On the estimation of inequalities by maximum and minimum values, Journal of College Arts and Science, Chiba University, 5(1968), 199-203.(in Japanese)
  • [13] P´olya, G., Szeg˝o, G., Problems and Theorems in Analysis. Vol. I: Series, Integral Calculus, Theory of Functions. Translated from the German by D. Aeppli Die Grundlehren dermathematischen Wissenschaften, Band 193. Springer-Verlag, New York-Berlin, 1972.
  • [14] Rad, N.J., Jahanbani, A., Gutman, I., Zagreb energy and Zagreb estrada index of graphs, MATCH Commun. Math. Comput. Chem., 79(2018), 371-386.
  • [15] Rada, J., Cruz, R., Gutman, I., Benzenoid systems with extremal vertex–degree–based topological indices, MATCH Commun. Math. Comput. Chem., 72(2014), 125-136.
  • [16] Shirdel, G.H., Rezapour, H., Sayadi, A.M., The hyper–Zagreb index of graph operations, Iran. J. Math. Chem., 4 (2013), 213-220.
  • [17] Shparlinski, I., On the energy of some circulant graphs, Linear Algebra and Its Applications, 414(2006), 378-382.
  • [18] Tian, G., Huang, T., A note on upper bounds for the spectral radius of weighted graphs, Appl. Math. Comput., 243(2014), 392-397.
  • [19] Wiener, H., Structural determination of paran boiling points, Journal of the American Chemical Society, 69(1947), 17-20.
  • [20] Yu, A., Lu, M., Lower bounds on the (Laplacian) spectral radius of weighted graphs, Chinese Annals of Mathematics, Series B, 35(2014), 669-678.
  • [21] Zhou, B., Trinajsti´c, N., On general sum-connectivity index, J. Math. Chem., 47(2009), 1252-1270.
Yıl 2021, Cilt: 13 Sayı: 1, 162 - 173, 30.06.2021

Öz

Destekleyen Kurum

Harran Üniversitesi Bilimsel Araştırma Projeleri Birimi (HUBAP)

Proje Numarası

21002

Kaynakça

  • [1] Büyükköse, Ş., Mutlu, N., Some bounds for the weighted energy, Sinop Uni. J. Nat. Sci., 1(2016), 62-65.
  • [2] Büyükköse, Ş., Mutlu, N., Nurkahlı S.B., Some bounds for the largest eigenvalue of weighted distance matrix and weighted distance energy, Journal of Science and Arts, 2(2017), 245-256.
  • [3] Consonni, V., Todeschini, R., New spectral index for molecule description, MATCH Communications in Mathematical and in Computer Chemistry, 60(2008), 3-14.
  • [4] Gutman, I., Trinajsti´c, N., Graph theory and molecular orbitals. Total -electron energy of alternant hydrocarbons, Chem. Phys. Lett.,17(1972), 535-538.
  • [5] Gutman, I., Ruscic, B., Trinajstic, N., Wilcox, C.F., Graph theory and molecular orbitals. XII. Acyclic polyenes, J. Chem. Phys. 62(1975), 3399-3405.
  • [6] Gutman, I., The energy of a graph. Berlin Mathmatics-Statistics Forschungszentrum, 103(1978), 1-22.
  • [7] Gutman, I., Polansky, O.E., Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
  • [8] He, C., Wang, W., Li, Y., Liu, L., Some Nordhaus-Gaddum type results of A$\alpha $ -eigenvalues of weighted graphs, Applied Mathematics and Computation, 393(2021), 1-10.
  • [9] Li, X., Shi, Y., Gutman, I., Graph Energy, Springer, New York, 2012.
  • [10] Li, X., Zhao, H., Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem., 50(2004), 57-62.
  • [11] Li, X., Zheng, J., A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem., 54(2005), 195-208.
  • [12] Ozeki, N., On the estimation of inequalities by maximum and minimum values, Journal of College Arts and Science, Chiba University, 5(1968), 199-203.(in Japanese)
  • [13] P´olya, G., Szeg˝o, G., Problems and Theorems in Analysis. Vol. I: Series, Integral Calculus, Theory of Functions. Translated from the German by D. Aeppli Die Grundlehren dermathematischen Wissenschaften, Band 193. Springer-Verlag, New York-Berlin, 1972.
  • [14] Rad, N.J., Jahanbani, A., Gutman, I., Zagreb energy and Zagreb estrada index of graphs, MATCH Commun. Math. Comput. Chem., 79(2018), 371-386.
  • [15] Rada, J., Cruz, R., Gutman, I., Benzenoid systems with extremal vertex–degree–based topological indices, MATCH Commun. Math. Comput. Chem., 72(2014), 125-136.
  • [16] Shirdel, G.H., Rezapour, H., Sayadi, A.M., The hyper–Zagreb index of graph operations, Iran. J. Math. Chem., 4 (2013), 213-220.
  • [17] Shparlinski, I., On the energy of some circulant graphs, Linear Algebra and Its Applications, 414(2006), 378-382.
  • [18] Tian, G., Huang, T., A note on upper bounds for the spectral radius of weighted graphs, Appl. Math. Comput., 243(2014), 392-397.
  • [19] Wiener, H., Structural determination of paran boiling points, Journal of the American Chemical Society, 69(1947), 17-20.
  • [20] Yu, A., Lu, M., Lower bounds on the (Laplacian) spectral radius of weighted graphs, Chinese Annals of Mathematics, Series B, 35(2014), 669-678.
  • [21] Zhou, B., Trinajsti´c, N., On general sum-connectivity index, J. Math. Chem., 47(2009), 1252-1270.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

N. Feyza Yalçın 0000-0001-5705-8658

Ahmet Kılıç 0000-0001-9073-4339

Proje Numarası 21002
Yayımlanma Tarihi 30 Haziran 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 13 Sayı: 1

Kaynak Göster

APA Yalçın, N. F., & Kılıç, A. (2021). Zagreb Energy of Weighted Graphs. Turkish Journal of Mathematics and Computer Science, 13(1), 162-173. https://doi.org/10.47000/tjmcs.886707
AMA Yalçın NF, Kılıç A. Zagreb Energy of Weighted Graphs. TJMCS. Haziran 2021;13(1):162-173. doi:10.47000/tjmcs.886707
Chicago Yalçın, N. Feyza, ve Ahmet Kılıç. “Zagreb Energy of Weighted Graphs”. Turkish Journal of Mathematics and Computer Science 13, sy. 1 (Haziran 2021): 162-73. https://doi.org/10.47000/tjmcs.886707.
EndNote Yalçın NF, Kılıç A (01 Haziran 2021) Zagreb Energy of Weighted Graphs. Turkish Journal of Mathematics and Computer Science 13 1 162–173.
IEEE N. F. Yalçın ve A. Kılıç, “Zagreb Energy of Weighted Graphs”, TJMCS, c. 13, sy. 1, ss. 162–173, 2021, doi: 10.47000/tjmcs.886707.
ISNAD Yalçın, N. Feyza - Kılıç, Ahmet. “Zagreb Energy of Weighted Graphs”. Turkish Journal of Mathematics and Computer Science 13/1 (Haziran 2021), 162-173. https://doi.org/10.47000/tjmcs.886707.
JAMA Yalçın NF, Kılıç A. Zagreb Energy of Weighted Graphs. TJMCS. 2021;13:162–173.
MLA Yalçın, N. Feyza ve Ahmet Kılıç. “Zagreb Energy of Weighted Graphs”. Turkish Journal of Mathematics and Computer Science, c. 13, sy. 1, 2021, ss. 162-73, doi:10.47000/tjmcs.886707.
Vancouver Yalçın NF, Kılıç A. Zagreb Energy of Weighted Graphs. TJMCS. 2021;13(1):162-73.