𝜇- Graph of a Finite Group

Rani Jose; Dr. Susha D

doi:https://doi.org/10.14445/22315373/IJMTT-V67I1P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 1 | Year 2021 | Article Id. IJMTT-V67I1P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I1P517

𝜇- Graph of a Finite Group

Rani Jose, Dr. Susha D

Abstract

𝜇 - graph of a finite group G is a graph whose vertex set is same as G itself and two vertices x, y are adjacent if and only if 𝜇 (|x| |y|) =𝜇 (| x|) 𝜇 (|y|) . The objective of this paper is to introduce 𝜇 − graph of a finite group and discuss some of its properties.

Keywords

Adjacency matrix, Eigen value, Energy, Mobius function, 𝜇 − graph of a finite group

References

[1] R. H Aravinth, R. Vignesh., Mobius Function Graph Mn (G), IJITEE , 8(10)(2019).
[2] R.Balakrishnan and K. Ranganathan , A Textbook of Graph Theory, Springer.
[3] R. B. Bapat, Graph And Matrices, Springer, Hindustan book agency.
[4] I. Gutman., The energy of regular graph, Ber.Math-Statist.Sekt.Forchungsz.Graz,103(1978) 1-22.
[5] I. N. Herstein, Topics in Algebra, Second Edition, John Wiley and Sons, (2003).
[6] Ma.X, Wei.H and Yang.L, The Coprime Graph of a Group, Int.J.Group Theory.,3(3)(2014) 13-23.
[7] K. R. Parthasarathy , Basic Graph Theory, Tata McGraw- Hill publishing company limited, New Delhi.
[8] Rodriguez Luke, Automorphism Groups of Simple Graphs.
[9] M. Sattanathan and R. Kala. An Introduction to order prime graphs, Int.J.Contemp.Math.Science, 4(10)(2009) 467-474.
[10] Tom M. Apostol, Introduction to analytic Number theory, Springer International Student Editor.

Citation :

Rani Jose, Dr. Susha D, "𝜇- Graph of a Finite Group," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 1, pp. 129-135, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I1P517