The Geodesic Polynomials in a Graph

Swamy; N. D. Soner; B. M. Chandrashekara

doi:https://doi.org/10.14445/22315373/IJMTT-V68I3P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 3 | Year 2022 | Article Id. IJMTT-V68I3P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I3P510

The Geodesic Polynomials in a Graph

Swamy, N. D. Soner, B. M. Chandrashekara

Citation :

Swamy, N. D. Soner, B. M. Chandrashekara, "The Geodesic Polynomials in a Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 3, pp. 52-58, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I3P510

Abstract

A shortest path between two vertices in a graph G is a geodesic in G A graph polynomial is a graph invariant. There are many graph polynomials can be found in the literature including, the characteristic polynomial, the chromatic polynomial and so on. This paper aims at the study of two new graph polynomials associated with the geodesics in a graph introduced by R. Rajendra and P.S.K. Reddy, namely, the geodesic polynomial of a graph and the geodesic polynomial at a vertex in a graph. We obtain some results involving geodesic polynomials of graphs and geodesic polynomials at the vertices

Keywords

Graph, geodesic, polynomial.

References

[1] Alsinai, A. Alwardi, H. Ahmed, & N.D. Soner, Leap Zagreb Indices for the Central Graph of Graph, Journal of Prime Research in Mathematics. 17(2) (2021) 73-78.
[2] F. Afzal, A. Alsinai, S. Hussain, D. Afzal, F. Chaudhry, & M. Cancan, On Topological Aspects of Silicate Network Using M-Polynomial. Journal of Discrete Mathematical Sciences and Cryptography. (2021) 1-1
[3] A. Alsinai, H. Ahmed, A. Alwardi, & N.D. Soner, HDR Degree Bassed Indices and MHR-Polynomial for the Treatment of COVID-19, Biointerface Research in Applied Chemistry. 12(6) (2021) 7214-7225.
[4] A. Alsinai, A. Alwardi, & N.D. Soner, On the ψk-polynomial of graph, Eurasian Chem. Commun. 3 (2021) 219-226.
[5] Alsinai A. Alwardi, & N.D. Soner, Topological Properties of Graphene Using YK Polynomial, In Proceedings of the Jangjeon Mathematical Society. 24(3) (2021).
[6] K. Bhargava, N. N. Dattatreya, and R. Rajendra, On Stress of a Vertex in a Graph, Palest. J. Math, Accepted for Publication.
[7] K. Bhargava N. N, Dattatreya, and R. Rajendra, Tension on an Edge in a Graph, Bol. Soc. Paran. Mat, Accepted for Publication.
[8] J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electron. J. Combin. DS6 (2019) 1–535.
[9] F. Harary, Graph Theory, Addison Wesley, Reading, Mass. (1972).
[10] Hasan, M.H.A . Qasmi, A. Alsinai, M. Alaeiyan, M.R. Farahani, & M. Cancan, Distance and Degree Based Topological Polynomial and Indices of X-Level Wheel Graph, Journal of Prime Research in Mathematics. 17(2) (2021) 39-50.
[11] S. Javaraju, A. Alsinai, A. Alwardi, H. Ahmed, & N.D. Soner, Reciprocal Leap Indices of Some Wheel Related Graphs, Journal of Prime Research in Mathematics. 17(2) (2021) 101-110.
[12] C. Kang, C. Molinaro, S. Kraus, Y. Shavitt, V. Subrahmanian, Diffusion Centrality in Social Networks, In Proceedings of the, International Conference on Advances in Social Networks Analysis and Mining ASONAM 2012, IEEE Computer Society. (2012) 558–564.
[13] D. Koschu¨tzki, K. A. Lehmann, L. Peeters, S. Richter, D. Tenfelde-Podehl and O. Zlotowsk, Centrality Indices, in Network Analysis, Lecture Notes in Computer Science, ed., Brandes U, Erlebach T, Springer, Berlin, Heidelberg. 3418 (2005) 16–61.
[14] R. Rajendra, P. S. K. Reddy and I. N. Cangul, Stress Indices of Graphs, Advn. Stud. Contemp. Math. 31(2) (2021) 163–173.
[15] R. Rajendra, P. S. K. Reddy, Smitha G Kini and M. Smitha, Peripheral Geodesic Index for graphs, Communicated for Publication
[16] G. Scardoni, M. Petterlini and C. Laudanna, Analyzing Biological Network Parameters with Centiscape, Bioinformatics. 25 (2009) 2857–2859.
[17] A. Shimbel, Structural Parameters of Communication Networks, Bulletin of Mathematical Biophysics. 15 (1953) 501-507.
[18] K. Shinozaki, Y.S. Kazuko and S. Motoaki, Regulatory Network of Gene Expression in the Drought and Cold Stress Responses, Curr. Opin. Plant Biol. 6(5) (2003) 410–417.