Minimum Dominating Extended Energy
[Full Text]
AUTHOR(S)
M. R. Rajesh Kanna, S. Roopa
KEYWORDS
Minimum dominating set, Extended matrix, Extended energy, Eigenvalues.
ABSTRACT
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.
REFERENCES
[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].
|