Perfect Non-Neighbor Harmonic Graphs

Authors

  • Rizwana A Dept. Mathematics, Manonmaniam Sundaranar University, Tirunelveli-12, India
  • Jeyakumar G Dept. of Mathematics, St.John’s College, Tirunelveli – 2, India
  • Mohamed Ismail M Dept. of Computer Application, the New College, Chennai-14, India

DOI:

https://doi.org/10.26438/ijcse/v6i10.555560

Keywords:

Graphs, non-neighbors, non-neighbor harmonic polynomial, perfect non-neighbor harmonic graphs

Abstract

Computation of topological indices is a recent research problem in mathematical and computational chemistry. Based on the number of non-neighbors of a vertex u in a graph G, non-neighbor harmonic index is defined. In this paper we compute the non-neighbor harmonic polynomial of some graphs. We develop a MATLAB program for computing the roots of the non-neighbor harmonic polynomial and hence define the perfect non-neighbor harmonic graphs.

References

[1] Narsing Deo, “Graph Theory with Applications to Engineering and Computer Science”, Prentice–Hall of India, Indian Reprint, New Delhi,

[2] Ivan Gutman, “Degree-based topological indices”, Croat. Chem. Acta, 86 (4) (2013) 251-361.

[3] Huiqing Liu, Mei Lu, Feng Tian, “On the Randic index”, Journal of Mathematical Chemistry Vol. 38, No. 3, October (2005).

[4] T.Doslic, “Vertex-Weighted Wiener Polynomials for Composite Graphs”, ARS MATHEMATICA CONTEMPORANEA 1 (2008) 66–80.

[5] A.R. Ashrafi, T. Doslic, A. Hamzeh, “The Zagreb coindices of graph operations”, Discrete Applied Mathematics 158 (2010) 1571-1578.

[6] A.R. Ashrafi, T. Doslic, A. Hamzeh, “Extremal Graphs with Respect to the Zagreb Coindices”, MATCH Commun. Math. Comput. Chem. 65 (2011) 85-92.

[7] Hongbo Hua, Shenggui Zhang, “Relations between Zagreb Coindices and Some Distance Based Topological Indices”, MATCH Commun. Math. Comput. Chem. 68 (2012) 199-208.

[8] Maolin Wang and Hongbo Hua, “More on Zagreb Coindices of Composite Graphs”, International Mathematical Forum, Vol. 7, 2012, No. 14, 669 – 673.

[9] P.S Ranjini, V. Lokesha, M. Bindusree and M. Phani Raju, “New Bounds on Zagreb indices and the Zagreb Co-indices”, Bol. Soc. Paran. Mat. (3s.) v. 31 1 (2013): 51–55.

[10] Douglas B.West, “Introduction to Graph Theory”, Second Edition, PHI Learning Private Limited, New Delhi.

[11] Lingping Zhong, “The harmonic index for Graphs”, Applied Mathematics Letters, 25(2012)561-566.

[12] A.Rizwana G,Jeyakumar, S.Somusundaram, “On Non-Neighbor Zagreb Indices and Non-Neighbor Harmonic Index”, International Journal of Mathematics And its Applications, Volume 4, Issue 2-D (2016), 89-101.

[13] Mohammad A. Iranmanesh and Mahboubeh Saheli, “On the harmonic index and harmonic polynomial of caterpillars with diameter four”, Iranian Journal of Mathematical Chemistry, Vol.6, No.1, March 2015; pp.41-49.

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Published

2025-11-17
CITATION
DOI: 10.26438/ijcse/v6i10.555560
Published: 2025-11-17

How to Cite

[1]
A. Rizwana, G. Jeyakumar, and M. Mohamed Ismail, “Perfect Non-Neighbor Harmonic Graphs”, Int. J. Comp. Sci. Eng., vol. 6, no. 10, pp. 555–560, Nov. 2025.

Issue

Vol. 6 No. 10 (2018): IJCSE October Edition

Section

Research Article

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