The M-polynomial of line graph of subdivision graphs

Sourav Mondal; Nilanjan De; Anita Pal

doi:10.31801/cfsuasmas.587655

Araştırma Makalesi

The M-polynomial of line graph of subdivision graphs

Yıl 2019, Cilt: 68 Sayı: 2, 2104 - 2116, 01.08.2019

Sourav Mondal Nilanjan De Anita Pal

https://doi.org/10.31801/cfsuasmas.587655

Cited By: 12

Öz

Three composite graphs Ladder graph (L_{n}), Tadpole graph (T_{n,k}) and Wheel graph (W_{n}) are graceful graphs, which have different applications in electrical, electronics, wireless communication etc. In this report, we first determine M-polynomial of the Line graph of those three graphs using subdivision idea and then compute some degree based indices of the same.

Anahtar Kelimeler

M-polynomial, degree based topological index, line graph, subdivision graph

Kaynakça

Deutsch, E. and Klavzar, S., M-Polynomial, and degree-based topological indices, Iran. J. Math. Chem., 6,(2015), 93-102.
Gutman, I., Some properties of the Wiener polynomials, Graph Theory Notes N.Y., 125, (1993), 13-18.
Alamian, V., Bahrami, A. and Edalatzadeh, B., PI Polynomial of V-Phenylenic nanotubes and nanotori, Int. J. Mole. Sci. 9(3), (2008), 229-234. doi: 10.3390/ijms9030229.
Farahani, MR., Computing theta polynomial, and theta index of V-phenylenic planar, nanotubes and nanotoris, Int. J. Theoretical Chem., 1(1), (2013), 01-09.
Munir, M., Nazeer, W., Shahzadi, S. and Kang , SM., Some invariants of circulant graphs, Symmetry, 8(11), (2016), 134. doi: 10.3390/sym8110134.
Rajan, M.A., Lokesha, V. and Ranjini, P.S., A Study on Series Edge Graph Transformation, Proc. 23rd Joint Congress Iran-South Korea Jangjeon Math. Soc.,Iran, (2010).
Ranjini, P.S., Lokesha, V. and Rajan, M.A., On Zagreb indices of the subdivision graphs, Int. J. Math. Sci. Eng. Appl., (2010), 4, 221-228.
Ranjini, P.S., Lokesha, V. and Rajan, M.A., On Zagreb indices of the p-subdivision graphs, J. Oriss. Math. Soc., (2010), appear.
Gutman, I., Lee, Y-N., Yeh Y.N. and Lau, Y.L., Some recent results in the theory of Wiener number, Ind. J. Chem., 32,(1993), 551-661.
Douglas, B.W., Introduction to Graph Theory, second ed., Prentice Hall, 2001.
Weisstein, E.W., Tadpole Graph, Mathworld-A Wolfram Web Resource.
Ranjini, P.S., Lokesha, V. and Cangıl, I.N., On the Zagreb indices of the line graphs of the subdivision graphs, Applied Mathematics and Computation, (2011), 218, 699-702.
Su, Guifu, Xu, Lan, Topological indices of the line graph of subdivision graphs and their Schur-bounds, Applied Mathematics and Computation, (2015), 395-401.
Gutman, I., Degree-based topological indices, Croat. Chem. Acta, 86, (2013), 351-361.
Gutman, I. and Trinajstic, N., Graph theory and molecular orbitals total Ï†-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17,(1972), pp. 535-538.
Bollobas, B. and Erdös, P., Graphs of extremal weights, Ars Combin., 50,(1998), pp.225-233.
Amic, D., Beslo, D., Lucic, B., Nikolic, S. and Trinajstiác, N., The vertex-connectivity index revisited, J. Chem. Inf. Comput. Sci., 38,(1998), pp. 819-822.
Hu, Y., Li, X., Shi, Y., Xu, T. and Gutman, I., On molecular graphs with smallest and greatest zeroth-Corder general Randiác index, MATCH Commun. Math. Comput.Chem., 54,(2005), pp. 425-434.
Caporossi, G., Gutman, I., Hansen, P. and Pavlovic, L., Graphs with maximum connectivity index, Comput. Biol. Chem., 27,(2003), pp. 85-90.
Li, X. and Gutman, I., Mathematical aspects of Randiac-type molecular structure descriptors, Mathematical Chemistry Monographs, No. 1, Publisher Univ. Kragujevac, Kragujevac, 2006.
Fajtlowicz, S., On conjectures of Graffiti II, Congr. Numer., 60,(1987), pp. 189-197.
Balaban, A. T., Highly discriminating distance based numerical descriptor, Chem.Phys. Lett., 89,(1982), pp. 399-404.
Furtula, B., Graovac, A. and Vukićević, D., Augmented Zagreb index, J. Math. Chem., 48 (2010), pp. 370-380.

Yıl 2019, Cilt: 68 Sayı: 2, 2104 - 2116, 01.08.2019

Sourav Mondal Nilanjan De Anita Pal

https://doi.org/10.31801/cfsuasmas.587655

Cited By: 12

Öz

Kaynakça

Deutsch, E. and Klavzar, S., M-Polynomial, and degree-based topological indices, Iran. J. Math. Chem., 6,(2015), 93-102.
Gutman, I., Some properties of the Wiener polynomials, Graph Theory Notes N.Y., 125, (1993), 13-18.
Alamian, V., Bahrami, A. and Edalatzadeh, B., PI Polynomial of V-Phenylenic nanotubes and nanotori, Int. J. Mole. Sci. 9(3), (2008), 229-234. doi: 10.3390/ijms9030229.
Farahani, MR., Computing theta polynomial, and theta index of V-phenylenic planar, nanotubes and nanotoris, Int. J. Theoretical Chem., 1(1), (2013), 01-09.
Munir, M., Nazeer, W., Shahzadi, S. and Kang , SM., Some invariants of circulant graphs, Symmetry, 8(11), (2016), 134. doi: 10.3390/sym8110134.
Rajan, M.A., Lokesha, V. and Ranjini, P.S., A Study on Series Edge Graph Transformation, Proc. 23rd Joint Congress Iran-South Korea Jangjeon Math. Soc.,Iran, (2010).
Ranjini, P.S., Lokesha, V. and Rajan, M.A., On Zagreb indices of the subdivision graphs, Int. J. Math. Sci. Eng. Appl., (2010), 4, 221-228.
Ranjini, P.S., Lokesha, V. and Rajan, M.A., On Zagreb indices of the p-subdivision graphs, J. Oriss. Math. Soc., (2010), appear.
Gutman, I., Lee, Y-N., Yeh Y.N. and Lau, Y.L., Some recent results in the theory of Wiener number, Ind. J. Chem., 32,(1993), 551-661.
Douglas, B.W., Introduction to Graph Theory, second ed., Prentice Hall, 2001.
Weisstein, E.W., Tadpole Graph, Mathworld-A Wolfram Web Resource.
Ranjini, P.S., Lokesha, V. and Cangıl, I.N., On the Zagreb indices of the line graphs of the subdivision graphs, Applied Mathematics and Computation, (2011), 218, 699-702.
Su, Guifu, Xu, Lan, Topological indices of the line graph of subdivision graphs and their Schur-bounds, Applied Mathematics and Computation, (2015), 395-401.
Gutman, I., Degree-based topological indices, Croat. Chem. Acta, 86, (2013), 351-361.
Gutman, I. and Trinajstic, N., Graph theory and molecular orbitals total Ï†-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17,(1972), pp. 535-538.
Bollobas, B. and Erdös, P., Graphs of extremal weights, Ars Combin., 50,(1998), pp.225-233.
Amic, D., Beslo, D., Lucic, B., Nikolic, S. and Trinajstiác, N., The vertex-connectivity index revisited, J. Chem. Inf. Comput. Sci., 38,(1998), pp. 819-822.
Hu, Y., Li, X., Shi, Y., Xu, T. and Gutman, I., On molecular graphs with smallest and greatest zeroth-Corder general Randiác index, MATCH Commun. Math. Comput.Chem., 54,(2005), pp. 425-434.
Caporossi, G., Gutman, I., Hansen, P. and Pavlovic, L., Graphs with maximum connectivity index, Comput. Biol. Chem., 27,(2003), pp. 85-90.
Li, X. and Gutman, I., Mathematical aspects of Randiac-type molecular structure descriptors, Mathematical Chemistry Monographs, No. 1, Publisher Univ. Kragujevac, Kragujevac, 2006.
Fajtlowicz, S., On conjectures of Graffiti II, Congr. Numer., 60,(1987), pp. 189-197.
Balaban, A. T., Highly discriminating distance based numerical descriptor, Chem.Phys. Lett., 89,(1982), pp. 399-404.
Furtula, B., Graovac, A. and Vukićević, D., Augmented Zagreb index, J. Math. Chem., 48 (2010), pp. 370-380.

Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Sourav Mondal 0000-0003-1928-7075 Nilanjan De 0000-0003-1928-7075 Anita Pal 0000-0002-2514-5463
Yayımlanma Tarihi	1 Ağustos 2019
Gönderilme Tarihi	5 Şubat 2018
Kabul Tarihi	25 Haziran 2019
Yayımlandığı Sayı	Yıl 2019 Cilt: 68 Sayı: 2

Kaynak Göster

APA	Mondal, S., De, N., & Pal, A. (2019). The M-polynomial of line graph of subdivision graphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 2104-2116. https://doi.org/10.31801/cfsuasmas.587655
AMA	Mondal S, De N, Pal A. The M-polynomial of line graph of subdivision graphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2019;68(2):2104-2116. doi:10.31801/cfsuasmas.587655
Chicago	Mondal, Sourav, Nilanjan De, ve Anita Pal. “The M-Polynomial of Line Graph of Subdivision Graphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 2 (Ağustos 2019): 2104-16. https://doi.org/10.31801/cfsuasmas.587655.
EndNote	Mondal S, De N, Pal A (01 Ağustos 2019) The M-polynomial of line graph of subdivision graphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 2104–2116.
IEEE	S. Mondal, N. De, ve A. Pal, “The M-polynomial of line graph of subdivision graphs”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 2, ss. 2104–2116, 2019, doi: 10.31801/cfsuasmas.587655.
ISNAD	Mondal, Sourav vd. “The M-Polynomial of Line Graph of Subdivision Graphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (Ağustos 2019), 2104-2116. https://doi.org/10.31801/cfsuasmas.587655.
JAMA	Mondal S, De N, Pal A. The M-polynomial of line graph of subdivision graphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:2104–2116.
MLA	Mondal, Sourav vd. “The M-Polynomial of Line Graph of Subdivision Graphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 2, 2019, ss. 2104-16, doi:10.31801/cfsuasmas.587655.
Vancouver	Mondal S, De N, Pal A. The M-polynomial of line graph of subdivision graphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):2104-16.