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IJSTR >> Volume 9 - Issue 3, March 2020 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Minimum Dominating Extended Energy

[Full Text]



M. R. Rajesh Kanna, S. Roopa



Minimum dominating set, Extended matrix, Extended energy, Eigenvalues.



In this manuscript we defined a new type of matrix called minimum dominating extended matrix and hence energy by using degree of a adjacent vertices. In this manuscript we have calculated minimum dominating extended energies for some standard graphs. Latterly, the manuscript lower and upper bounds for this extended energy are also obtained.



[1] C. Adiga, A. Bayad, I. Gutman and S. A. Srinivas, The minimum covering energy of a graph,Kragujevac J. Sci., 34, (2012), 39 - 56.
[2] R. B. Bapat, page No.32, Graphs and Matrices, Hindustan Book Agency, (2011)
[3] I. Gutman, The energy of a graph, Ber. Math-tatist. Sekt. Forschungsz. Graz, 103, (1978), 1-22.
[4] I. Gutman, 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), 196 - 211.
[5] J.H. Koolen and V. Moulton, Maximal energy graphs.Adv.Appl. Math., 26, 47-52 (2001).
[6] B. J. MClelland, Properties of the latent roots of a matrix: The estimation of -electron energies, J. Chem. Phys., 54, 640 - 643 (1971).
[7] I. _Z. Milovanovi_c, E. I. Milovanovi_c and A. Zaki_c, A Short note on Graph Energy, MATH Commun. Math.Comput. Chem., 72, (2014), 179-182.
[8] Y. Q. Yang, L.Xu, C.Y.Hu, Extended adjacency matrix indices and their applications, J. Chem.Inf.Comput.Sci.34,1994, 1140-1145.
[9] M. R. Rajesh Kanna, B. N. Dharmendra and G. Sridhara, Minimum dominating energy of a graph. International Journal of Pure and Applied Mathematics, 85, No. 4(2013) 707-718. [http://dx.doi.org/10.12732/ijpam.v85i4.7].