Back
 ALAMT  Vol.6 No.4 , December 2016
Minimum Covering Randić Energy of a Graph
Abstract: Randić energy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randić energy REC (G) of a graph G in this paper. This paper contains computation of minimum covering Randić energies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randić energy are also presented.
Cite this paper: Kanna, M. , Jagadeesh, R. (2016) Minimum Covering Randić Energy of a Graph. Advances in Linear Algebra & Matrix Theory, 6, 116-131. doi: 10.4236/alamt.2016.64012.
References

[1]   Bozkurt, S.B., Güngör, A.D. and Gutman, I. (2010) Randić Spectral Radius and Randić Energy. Communications in Mathematical and in Computer Chemistry, 64, 239-250.

[2]   Gutman, I. (1978) The Energy of a Graph. Ber. Math-Statist. Sekt. Forschungsz. Graz, 103, 1-22.

[3]   Gutman, I., Li, X. and Zhang, J. (2009) Graph Energy. In: Dehmer, M. and Emmert-Streib, F., Eds., Analysis of Complex Networks. From Biology to Linguistics, Wiley-VCH, Weinheim, 145-174.

[4]   Cvetković, D. and Gutman, I., Eds. (2009) Applications of Graph Spectra. Mathematical Institution, Belgrade.

[5]   Cvetković, D. and Gutman, I., Eds. (2011) Selected Topics on Applications of Graph Spectra. Mathematical Institute Belgrade.

[6]   Gutman, I. (2001) The Energy of a Graph: Old and New Results. In: Betten, A., Kohnert, A., Laue, R. and Wassermann, A., Eds., Algebraic Combinatorics and Applications, Springer, Berlin, 196-211.

[7]   Liu, H.Q., Lu, M. and Tian, F. (2007) Some Upper Bounds for the Energy of Graphs. Journal of Mathematical Chemistry, 41, 45-57.
https://doi.org/10.1007/s10910-006-9183-9

[8]   McClelland, B.J. (1971) Properties of the Latent Roots of a Matrix: The Estimation of π - Electron Energies. The Journal of Chemical Physics, 54, 640-643.
https://doi.org/10.1063/1.1674889

[9]   Gutman, I. and Polansky, O.E. (1986) Mathematical Concepts in Organic Chemistry. Springer, Berlin.
https://doi.org/10.1007/978-3-642-70982-1

[10]   Graovac, A., Gutman, I. and Trinajstić, N. (1977) Topological Approach to the Chemistry of Conjugated Molecules. Springer, Berlin.
https://doi.org/10.1007/978-3-642-93069-0

[11]   Randić, M. (1975) On Characterization of Molecular Branching, Journal of the American Chemical Society, 97, 6609-6615.
https://doi.org/10.1021/ja00856a001

[12]   Bozkurt, S.B. and Bozkurt, D. (2013) Sharp Upper Bounds for Energy and Randić Energy. Communications in Mathematical and in Computer Chemistry, 70, 669-680.

[13]   Dilek Maden, A. (2015) New Bounds on the Incidence Energy, Randić Energy and Randić Estrada Index. Communications in Mathematical and in Computer Chemistry, 74, 367-387.

[14]   Das, K.Ch., Sorgun, S. and Gutman, I. (2015) On Randić Energy. Communications in Mathematical and in Computer Chemistry, 73, 81-92.

[15]   Adiga, C., Bayad, A., Gutman, I. and Srinivas, S.A. (2012) The Minimum Covering Energy of a Graph. Kragujevac Journal of Science, 34, 39-56.

[16]   Bapat, R.B. (2011) Graphs and Matrices. Hindustan Book Agency, Gurgaon, No.32.

[17]   Koolen, J.H. and Moulton, V. (2001) Maximal Energy Graphs. Advances in Applied Mathematics, 26, 47-52.
https://doi.org/10.1006/aama.2000.0705

[18]   Milovanović, I.Z., Milovanović, E.I. and Zakić, A. (2014) A Short Note on Graph Energy. MATCH Communications in Mathematical and in Computer Chemistry, 72, 179-182.

[19]   Biernacki, M., Pidek, H. and Ryll-Nadzewski, C. (1950) Sur une inequalite entre des inegrales defnies. Annales Universitatis Mariae Curie-Sklodowska Sectio A, 4, 1-4.

[20]   Diaz, J.B. and Matcalf, F.T. (1963) Stronger Forms of a Class Inequalities of G. Polja-G. Szego and L. V. Kantorovich. Bulletin of the American Mathematical Society, 69, 415-418.
https://doi.org/10.1090/S0002-9904-1963-10953-2

[21]   Bapat, R.B. and Pati, S. (2011) Energy of a Graph Is Never an Odd Integer. Bulletin of Kerala Mathematics Association, 1, 129-132.

 
 
Top