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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 29 | Number 1 | Year 2016 | Article Id. IJMTT-V29P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V29P501

Distance Energy of Certain Mesh Derived Networks and Milovanović Bounds


M.R. Rajesh Kanna, R. Jagadeesh , R. Pradeep Kumar, R.A Ramyashree
Citation :

M.R. Rajesh Kanna, R. Jagadeesh , R. Pradeep Kumar, R.A Ramyashree, "Distance Energy of Certain Mesh Derived Networks and Milovanović Bounds," International Journal of Mathematics Trends and Technology (IJMTT), vol. 29, no. 1, pp. 1-8, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V29P501

Abstract

In this paper, we compute the distance energy of grid, cylinder, torus, extended grid networks by using matlab. Also we obtained Milovanović bounds for distance energy of a graph.

Keywords
Distance matrix, Distance energy, Grid, Cylinder, Torus, Extended grid, Milovanović bounds.
References

[1] Bharati Rajan, Sudeep Stephen, Albert William, Cyriac Grigorous, On Laplacian Energy of Certain Mesh Derived Networks, International Journal of Computer Applications, Vol. 55- No.11, (2012).
[2] D.Cvetkovic, I. Gutman (eds.), Applications of Graph Spectra (Mathematical Institution, Belgrade,2009)
[3] D. Cvetkovic, I. Gutman (eds.) Selected Topics on Applications of Graph Spectra, (Mathematical Institute Belgrade,2011).
[4] I. Gutman, The energy of a graph.Ber. Math-Statist. Sekt. Forschungsz.Graz 103,1-22 (1978).
[5] I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer, Berlin,1986).
[6] I. Gutman, in The energy of a graph: Old and New Results,ed.by A. Betten, A. Kohnert, R. Laue, A. Wassermann. Algebraic Combinatorics and applications (Springer, Berlin, 2001), pp. 196 - 211.
[7] R. L. Graham, H. O. Pollak, On the addressing problem for loop switching, Bell System Tech.J. 50 (1971) 2495-2519.
[8] H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya, H. B.Walikar, Bounds for the distance energy of a graph, Kragujevac J. Math., 31 (2008), 59-68.
[9] I. Ž. Milovanović, E. I. Milovanović, A. Zakić, A Short note on Graph Energy, MATH Commun. Math. Comput. Chem, 72 (2014) 179-182.
[10] G. Indulal, I. Gutman, A. Vijaykumar, On the distance energy of a graph, MATCH Commun. Math. Comput. Chem. 60 (2008), 461-472.

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