Adjacency and Degree of Graph of Mobius Function

K. K. Srimitra*, Shaik Sajana**, D. Bharathi***
*-** Research Scholar, Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India.
*** Associate Professor, Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India.
Periodicity:January - March'2016
DOI : https://doi.org/10.26634/jmat.5.1.4869

Abstract

In this paper, the authors have consider the graph of Mobius function for zero, G(µn(0)). For an integer n≥1, the graph of Mobius function for zero is a graph with vertex set {1, 2, 3, …, n} and an edge, between two vertices a,b if the Mobius function value, µ(ab)=0. The authors have studied the basic results of a graph as the degree of vertex, the adjacency of two vertices and the planarity. First, the authors have calculated the minimum degree and the maximum degree of graph of Mobius function for '0'. The sufficient conditions for two vertices to be adjacent in the graph of Mobius function for '0' based on the divisibility of numbers are discussed and also, proved the necessary and sufficient condition for adjacency of two consecutive vertices in the graph of Mobius function for '0'. At the end, the authors have discussed the planarity of the graph according to the number of vertices of the graph.

Keywords

Mobius Function, Graph of Mobius Function, Degree, Adjacency.

How to Cite this Article?

Srimitra,K.K., Sajana,S., and Bharathi,D. (2016). Adjacency and Degree of Graph of Mobius Function. i-manager’s Journal on Mathematics, 5(1), 31-38. https://doi.org/10.26634/jmat.5.1.4869

References

[1]. Anderson D. F., and Badawi A, (2008). “The Total Graph of Commutative Ring”. Journal on Algebra, Vol.320, pp.2706- 2719.
[2]. Bharathi D., and Shaik Sajana, (2015). “Some Properties of the Intersection Graph for Finite Commutative Rings”. International Journal of Scientific and Innovative Mathematical Research, Vol.3(3), pp.1062-1066.
[3]. Bondy J. A. and Murthy. U. S. R, (1976). Graph Theory with Applications. Macmillan, London.
[4]. Cadogan C. C, (1971). “The Mobius Function and Connected Graphs”. Journal of Combinatorial Theory, Vol.11, pp.193-200.
[5]. Chalapathi T, and Madhavi L, (2013). “Enumeration of Triangles in a Divisor Cayley Graph”. Momona Ethiopian Journal of Science (MEJS), Vol.5(1), pp.163-173.
[6]. Douglas B. West, (2003). Introduction to Graph Theory. Second edition, Prentice Hall of India.
[7]. Eswara Rao D., and Bharathi D., (2014). “Total Graphs of Idealization”. International Journal of Computer Applications, Vol.87(15).
[8]. Melvyn B. Nathanson, (2006). Methods in Number Theory. Springer – Verlag New York, Inc.
[9]. Narsingh Deo, (2000). Graph Theory with Applications to Engineering and Computer Science. Prentice Hall Inc., U. S. A.
[10]. Nathanson Melvyn. B, (1980). “Connected Components of Arithmetic Graphs”. Monatshefte fur Mathematik, Vol.89, pp.219-222.
[11]. Tom M. Apostol, (1998). Introduction to Analytic Number Theory. Narosa publishing House.
[12]. Vasumathi. N, (1994). “Graphs on Numbers”. Ph.D. Thesis, Sri Venkateswara University, Tirupati, India.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.