Milovanovi´ c bounds for minimum dominating energy of a graph

G. Sridhara; M. R. Rajesh Kanna; B. N. Dharmendra

doi:10.26637/mjm302/012

Abstract

Recently Milovanović et.al gave a sharper lower bounds for energy of a graph. In this paper similar bounds for minimum dominating energy and Laplacian minimum dominating energy of a graph are established.

Keywords:

Minimum dominating energy, Minimum covering energy, Laplacian minimum dominating energy, Laplacian Minimum covering energy

Mathematics Subject Classification:

05C50, 05C69

Authors Imprint References Funding Related Articles Downloads

G. Sridhara Postgraduate Department of Mathematics, Maharani’s Science College for Women,J. L. B. Road, Mysore - 570 005, India.
M. R. Rajesh Kanna Postgraduate Department of Mathematics, Maharani’s Science College for Women,J. L. B. Road, Mysore - 570 005, India.
B. N. Dharmendra Postgraduate Department of Mathematics, Maharani’s Science College for Women,J. L. B. Road, Mysore - 570 005, India. https://orcid.org/0000-0001-9336-7562

Pages: 211-215
Date Published: 01-04-2015
Vol. 3 No. 02 (2015): Malaya Journal of Matematik (MJM)

C. Adiga, A. Bayad, 1. Gutman, S. A. Srinivas, The minimum covering energy of a graph. Kragujecuc J. Sci. $34(2012) 39-56$

A.Graovac, I.Gutman, N.Trinajstic, Topologionl Approach to the Chenristry of Conjugated Molecules (Springer, Berlin,1977) DOI: https://doi.org/10.1007/978-3-642-93069-0

LGutman, The energy of a graph. Ber. Math-Statist. Sekt. Forschangsz.Graz 103, 1-22 (1978)

I.Gutman, X, Li, J.Zhang, Graph Energy,ed. by M.Dehmer, F.Emmert - Streib. Analysis of Conplex Netmorks. From Biology to Linguistics (Wiley - VCH, Weinheim, 2009),pp. $145-174$. DOI: https://doi.org/10.1002/9783527627981.ch7

I.Gutman, The energy of a graph: Old and New Results, (Ed-s: A. Betten, A. Kohnert, R. Laue, A. Wassermann). Algebraic Combinatorics and Applications, Springer, Berlin(2001), Pp. 196 - 211. DOI: https://doi.org/10.1007/978-3-642-59448-9_13

I.Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer, Berlin,1986) DOI: https://doi.org/10.1515/9783112570180

Huiqing Liu, Mei Lu and Feng Tian, Some upper bounds for the energy of graphs Journal of Mathenatical Chemistry, Vol, 41, No.1, (2007). DOI: https://doi.org/10.1007/s10910-006-9183-9

B.J.McClelland, Properties of the latent roots of a matrix: The estimation of $pi$-electron energies. ]. Chem. Phys. 54, $640-643(1971)$ DOI: https://doi.org/10.1063/1.1674889

I. Z. Milovanovic,. E. I. Milovanović, A. Zakić, A Short note on Graph Energy, MATH Commun. Math. Comput. Chem, 72 (2014) 179-182.

M.R.Rajesh Kanna, B. N. Dharmendra, and G. Sridhara, Minimum Dominating Energy of a Graph. International Joural of Pare and Appled Mathenatics, 85, No. 4 (2013) 707-718.[ http://dx.doi.org $/ 10.12732 /$ ijpams.v85i4.7] DOI: https://doi.org/10.12732/ijpam.v85i4.7

M.R.Rajesh Kanna, B. N. Dhamendra, and G. Sridhara, Laplacian Minimum Dominating Energy of a Graph. International Journal of Pare and Applied Mathematics, 89, No. 4 (2013) 565-581.I http://dx.doi.org/10,12732/ipams.v89i4,11] DOI: https://doi.org/10.12732/ijpam.v89i4.11

M. R. Rajesh Kanna, B. N. Dharmendra, and G. Sridhara, Laplacian Minimum covering energy of a graph. Adonnces and Applications in Mathematics, 13, No. 2 (2014) 85-108.

The second author is thankful to the University Grants Commission, Government of India for the financial support under the grant MRP(S)-0535/13-14/KAMY004/UGC-SWRO.