Title: Energy of Prime Graphs and its Bounds
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-21-00018; Volume 3 / Issue 2 / Year 2021, Pages 29-37
Document Type: Research Paper
Author(s): Chandrashekar Adiga a , Anitha Narasimhamurthy
b , Mungara Deepthi Rao
c
aDepartment of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru-570 006, INDIA and Adjunct Professor, Adichunchanagiri University, Bengaluru – Hassan National Highway (NH-75), Nagamangala Taluk, B G Nagara – 571 448, Mandya District, INDIA
bDepartment of Science and Humanities, PES University, 100ft. Ring Road, BSK 3rd Stage, Bengaluru – 560085, INDIA
cDepartment of Science and Humanities, PES University, 100ft. Ring Road, BSK 3rd Stage, Bengaluru – 560085, INDIA
Received: 25 January 2021, Accepted: 9 March 2021, Published: 31 March 2021.
Corresponding Author: Chandrashekar Adiga (Email address: c_adiga@hotmail.com)
Full Text: PDF
Abstract
The special properties of factorization of primes makes it vitally important to communication. The RSA encryption system uses prime numbers to encrypt data. Motivated by the work on Fibonacci graph by Adiga et al.[1], in this paper we define a prime graph and examine its eigenvalues and obtain upper and lower bounds for the energy of the prime graph.
Keywords: Prime graph, Energy of a graph, Bounds for energy of a graph, Ramanujan graph
References:- C. Adiga, N. Anitha and H. C. Savith, Fibonacci graph and its energies, Adv. Stud. Contemp. Math. 31, 107-122, 2021.
- M. Biernacki, H. Pidec and C. Ryll-Nardzewski, Sur une inegalite enre des inteerales definies, Univ. Marie Curie-Sktodowska A (4), 1-4, 1950.
- K. Das, S. A. Mojallal and I. Gutman, Improving McClellands lower bound for energy, MATCH Commun. Math. Comput. Chem. 70, 663-668, 2013.
- K. Das and S. A. Mojallal, Upper bounds for the energy of graphs, MATCH Commun. Math. Comput. Chem. 70, 657-662, 2013.
- J. B. Diaz and F. T. Metclaf, Stronger forms of a class of inequalities of G. Polya-G, Szego and L. V. Kantorovich, Bull. Amer. Math. Soc. 69, 415-418, 1963.
- P. Dusart, Estimates of some functions over primes without R.H., arXiv:1002.044v1, 2010.
- A. Jahanbani, Lower bounds for the energy of graphs, AKCE Int. J. Graphs Comb. 15 (1), 88-96, 2018.
- X. Li, Y. Shi and I. Gutman, Graph Energy, Springer, New York, 2012.
- B. J. McClelland, Properties of the latent roots of a matrix: The estimation of π-electron energies, J. Chem. Phys. 4, 640–643, 1971.