On the ψk-polynomial of graph

Alsinai, Ammar; Alwardi, Anwar; Farahani, Mohammad Reza; Soner, Nandappa D.

doi:10.22034/ecc.2021.274069.1138

Document Type : Original Research Article

Authors

¹ Department of Studies in Mathematics University of Mysore, Manasagangotri Mysuru-570 006, India

² Department of Mathematics, University of Aden, Yemen

³ Department of Applied Mathematics, Iran University of Science and Technology (IUST), Narmak, Tehran 16846, Iran

https://doi.org/10.22034/ecc.2021.274069.1138

Abstract

In this paper, for every k-degree distance we define ψ_k-Polynomial of a connected graph G=(V,E) as where ψ_k(i,j) is the number of edges uv in G such that {d_k(v), d_k(u)}={i,j} and d_k(v), d_k(u) are the k^th degree distance of v and u, and δ_k, ∆_k are the minimum and maximum k^th distance degrees respectively. We compute the ψ2-Polynomial of some standard graphs and some graph operations. Also ψ2-Polynomial for honeycomb network and Graphene are obtained with their plotting in 3D.

Graphical Abstract

Keywords

References

[1] F. Afzal, M.A. Razaq, D. Afzal, S. Hameed, Eurasian Chem. Commun., 2020, 2, 652-662. [crossref], [Google Scholar], [Publisher]

[2] D. Afzal, S. Hussain, M. Aldemir, M. Farahani, F. Afzal, Eurasian Chem. Commun., 2020, 2, 1117–1125. [crossref], [Google Scholar], [Publisher]

[3] F. Afzal, S. Hussain, D. Afzal, S. Razaq, J. Inf. Opt. Sci., 2020, 41, 1061–1076. [crossref], [Google Scholar], [Publisher]

[4] Z. Ahmad, M. Naseem, M.K. Jamil, Sh. Wang, M.F. Nadeem, Eurasian Chem. Commun., 2020, 2, 712-721. [crossref], [Google Scholar], [Publisher]

[5] Z. Ahmad, M. Naseem, M.K. Jamil, M.K. Siddiqui, M.F. Nadeem, Eurasian Chem. Commun., 2020, 2, 663-671. [crossref], [Google Scholar], [Publisher]

[6] M. Alaeiyan, C. Natarajan, G. Sathiamoorthy, M.R. Farahani, Eurasian Chem. Commun., 2020, 2, 646-651. [crossref], [Google Scholar], [Publisher]

[7] M. Alaeiyan, A. Bahrami, M.R. Farahani, Dig. J. Nanomater. Bio., 2011, 6, 143-147.

[8] S. Akhter, M. Imran, W. Gao, M.R. Farahani, Hacet. J. Math. Stat., 2018, 47, 19–35. [crossref], [Google Scholar], [Publisher]

[9] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, The Macmillan Press Ltd, 1976, 535-538.

[10] E. Deutsch, S. Klavžar, Iran. J. Math. Chem, 2015, 1, 93–102. [crossref], [Google Scholar], [Publisher]

[11] M.R. Farahani, Acta Chim. Slov., 2012, 59, 965-968. [crossref], [Google Scholar], [Publisher]

[12] M.R. Farahani, World Appl. Sci. J., 2012, 20, 1248-1251. [crossref], [Google Scholar], [Publisher]

[13] M.R. Farahani, Int. J. Theor. Chem., 2013, 1, 01-09.

[14] M.R. Farahani, Chem. Phys. Res. J., 2013, 6, 27-35.

[15] M.R. Farahani, W. Gao, J Chem Pharm Res., 2015, 7, 535-539.

[16] M.R. Farahani, J. Chem. Acta., 2013, 2, 22-25.

[17] W. Gao, M.R. Farahani, J. Nanotechnol., 2016, 2016, 1-6. [crossref], [Google Scholar], [Publisher]

[18] W. Gao, M.R. Farahani, M.K. Jamil, Acta Chim. Slov., 2016, 63, 376-379. [crossref], [Google Scholar], [Publisher]

[19] H. Ahmed, A. Alwardi, R. Salestina M., N.D. Soner, J. Dis. Math. Sci. Cryp., 2021, 24, 325-341. https://doi.org/10.1080/09720529.2021.1882155

[20] H. Ahmed, A. Alwardi, R. Salestina M., Int.l J. Anal. Appl., 2020, 19, 47-64. [crossref], [Google Scholar], [Publisher]

[21] F. Harary, Graph Theory, Addison Wesley, Reading Mass, 1969.

[22] Y. Hong, J. East China Norm. Univ. Natur. Sci. Ed, 1986, 1, 31–34.

[23] W. Lin, J. Wu, P.C.B. Lam, G. Gu, Discrete Appl. Math, 2006, 15, 1173–1182. [crossref], [Google Scholar], [Publisher]

[24] A. Miličević, S. Nikolić, Croat. Chem. Acta, 2004,77, 97-101.

[25] M.S. Ahmad, S.M. Kang, C.Y. Jung, Pure Appl. Math., 2017, 6, 2749-2776.

[26] M. Munir, W. Nazeer, A.R. Nizami, S. Rafique, S.M. Kang, M- Symmetry, 2016, 8, 117-122. [crossref], [Google Scholar], [Publisher]

[27] M. Munir, W. Nazeer, S. Shahzadi, S.M. Kang, Symmetry, 2016, 8, 134-140. [crossref], [Google Scholar], [Publisher]

[28] H. Siddiqui, M.R. Farahani, Open J. Math. Anal., 2017, 1, 44–59. [crossref], [Google Scholar], [Publisher]

[29] I. Stojmenovic, Lect. Notes Comput. Sci., 1995, 969, 267-276.

[30] G. Sridhara, M.R. Rajesh Kanna, R.S. Indumathi, J. Nonmaterial., 2015, 2, Article ID 969348, 1-9. [crossref], [Google Scholar], [Publisher]

[31] I. Stojmenovic, IEEE Trans. Parallel. Distrib. Syst., 1997, 8, 1036-1042. [crossref], [Google Scholar], [Publisher]

[32] P.J.N. Thayamathy, P. Elango, M. Koneswaran, Int. Res. J. Pure. Appl Chem., 2018, 1-9.

[33] D.B. West, An Introduction to Graph Theory, Prentice-Hall, 1996.

[34] H. Zhang, F. Zhang, Appl. Math, 1996, 69, 147–167. [crossref], [Google Scholar], [Publisher]

[35] Z. Shao, A.R. Virk, M.S. Javed, M.A. Rehman, M.R. Farahani, Eng. Appl. Sci. Lett. 2019, 2, 01-11. [crossref], [Google Scholar], [Publisher]

Eurasian Chemical Communications

On the ψk-polynomial of graph

References

References

Volume 3, Issue 4
April 2021
Pages 219-226

On the ψk-polynomial of graph

References

References

Volume 3, Issue 4April 2021Pages 219-226

Volume 3, Issue 4
April 2021
Pages 219-226