MINIMUM COVERING GUTMAN ENERGY OF A GRAPH
DOI:
https://doi.org/10.20319/mijst.2019.51.0111Keywords:
Minimum Covering Gutman Energy, Minimum Covering Gutman Matrix, Minimum Covering Set, Upper BoundAbstract
The concept of a new kind of graph energy, namely, minimum covering energy, denoted by Ec(G), was introduced by Chandrashekar Adiga et.al in 2012. The Gutman energy is the sum of the absolute values of the eigenvalues obtained from the Gutman matrix. In this paper, we depict the minimum covering Gutman energy of a graph which can be defined as sum of the absolute values of the minimum covering Gutman eigenvalues obtained from the minimum covering Gutman matrix of a graph. Further, we establish the upper and lower bounds for minimum covering Gutman energy.
References
Adiga, C., Bayad, A., Gutman, I., and Srinivas, S.A.(2012).The minimum covering energy of a graph. Kragujevac J. Sci., 34, 39 - 56. http://shodhganga.inflibnet.ac.in/bitstream/10603/74800/9/chapter%206.pdf
Balakrishnan, R. (2004), The energy of a graph, Lin. Algebra Appl. 387, 287–295. https://www.sciencedirect.com/science/article/pii/S0024379504001259
Bapat, R.B.(2011). Graphs and Matrices, page no. 32, Hindustan Book Agency. https://www.springer.com/in/book/9781447165682
Gutman, I. (1978). The energy of a graph. Ber.Math. Stat. Sekt. Forschungsz.Graz 103, 122.
Liu, H., Lu, M., and Tian, F. (2007). Some upper bounds for the energy of graphs. Journal of Mathematical Chemistry, 41:1. https://link.springer.com/article/10.1007/s10910-006-9183-9
Rajesh, Kanna, M.R., Dharmendra, B, N., Pradeep, Kumar, R. (2013). Minimum Covering Distance Energy of a Graph. Applied Mathematical Sciences, Vol. 7, No. 111, 5525 - 5536. http://dx.doi.org/10.12988/ams.2013.38477
Roshan Sara Philipose, Sarasija P. B. (2018). Gutman Index and Harary Index of Unitary Cayley Graphs. International Journal of Engineering & Technology, 7 (3) (2018) 1243-1244. https://www.sciencepubco.com/index.php/ijet/article/view/13269/6112
Roshan Sara Philipose, Sarasija, P.B. (2018). Gutman Matrix and Gutman Energy of a Graph. Mathematical Sciences International Research Journal[Special Issue], Vol.7, 63-66.
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