Laplacian Minimum Covering Randic Energy of A Graph

M.R. Rajesh Kanna, R. Jagadeesh

Abstract


Randic energy was first defined in the article [6]. Using minimum covering set, we have introduced in this article Laplacian minimum covering Randic energy \(LRE_C(G)\) of a graph \(G\). This article contains computation of Laplacian minimum covering Randic energies for some standard graphs like star graph, complete graph, crown graph, complete bipartite graph and cocktail graph. At
the end of this article upper and lower bounds for Laplacian minimum covering Randic energy are also presented.

Keywords


Minimum covering set; Minimum covering Randic matrix; Laplacian minimum covering Randic matrix; Laplacian minimum covering Randic eigenvalues; Laplacian minimum covering Randic energy

Full Text:

PDF

References


C. Adiga, A. Bayad, I. Gutman and S.A. Srinivas, The minimum covering energy of a graph, Kragujevac J. Sci. 34 (2012), 39 – 56.

T. Aleksic, Upper bounds for Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), 435 – 439.

R.B. Bapat, Graphs and Matrices, page 32, Hindustan Book Agency (2011).

R.B. Bapat and S. Pati, Energy of a graph is never an odd integer, Bull. Kerala Math. Assoc. 1 (2011), 129 – 132.

M. Biernacki, H. Pidek and C. Ryll-Nadzewski, Sur une inequalite entre des inegrales defnies, Annales Univ. Marie Curie-Sklodowska A4 (1950), 1 – 4.

S.B. Bozkurt, A.D. Güngör and I. Gutman, Randic spectral radius and Randic energy, Commun. Math. Comput. Chem. 64(2010), 239 – 250.

S.B. Bozkurt and D. Bozkurt, Sharp upper bounds for energy and Randic energy, Commun. Math. Comput. Chem. 70 (2013), 669 – 680.

V. Consonni and R. Todeschini, New spectral index for molecule description, MATCH Commun. Math. Comput. Chem. 60 (2008), 3 – 14.

D. Cvetkovic and I. Gutman (eds.), Applications of Graph Spectra, Mathematical Institution, Belgrade (2009).

D. Cvetkovic and I. Gutman (eds.), Selected Topics on Applications of Graph Spectra, Mathematical Institute Belgrade (2011).

N.N.M. de Abreu, C.T.M. Vinagre, A.S. Bonifácio and I. Gutman, The Laplacian energy of some Laplacian integral graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), 447 – 460.

A. Dilek Maden, New bounds on the incidence energy, Randic energy and Randic Estrada index, Commun. Math. Comput. Chem. 74 (2015), 367 – 387.

J.B. Diaz and F.T. Matcalf, Stronger forms of a class inequalities of G. Polja-G. Szego and L.V. Kantorovich, Bull. Amer. Math. Soc. 69 (1963), 415 – 418.

G.H. Fath-Tabar, A.R. Ashrafi and I. Gutman, Note on Laplacian energy of graphs, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.) 137 (2008), 1 – 10.

A. Graovac, I. Gutman and N. Trinajstic, Topological Approach to the Chemistry of Conjugated Molecules Springer, Berlin (1977).

I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz 103 (1978), 1 – 22.

I. Gutman, The energy of a graph: old and new results, edited by A. Betten, A. Kohnert, R. Laue and A. Wassermann, Algebraic Combinatorics and Applications, Springer, Berlin (2001), pp. 196 – 211.

I. Gutman, N.M.M. de Abreu, C.T.M. Vinagre, A.S. Bonifácio and S. Radenkovic, Relation between energy and Laplacian energy, MATCH Commun. Math. Comput. Chem. 59 (2008), 343 – 354.

I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin (1986).

I. Gutman, X. Li and J. Zhang, in Graph Energy, edited by M. Dehmer and F. Emmert-Streib, Analysis of Complex Networks, from Biology to Linguistics, Wiley-VCH, Weinheim (2009), pp. 145 – 174.

I. Gutman and B. Zhou, Laplacian energy of a graph, Lin. Algebra Appl. 414 (2006), 29 – 37.

H. Liu, M. Lu and F. Tian, Some upper bounds for the energy of graphs, Journal of Mathematical Chemistry 41(1) (2007).

B.J. McClelland, Properties of the latent roots of a matrix: The estimation of (pi)-electron energies, J. Chem. Phys. 54 (1971), 640 – 643.

I. Ž. Milovanovic, E.I. Milovanovic and A. Zakic, A short note on graph energy, Commun. Math. Comput. Chem. 72 (2014), 179 – 182.

K.C. Das, S. Sorgun and I. Gutman, On Randic energy, Commun. Math. Comput. Chem. 73 (2015), 81 – 92.

J.H. Koolen and V. Moulton, Maximal energy graphs, Adv. Appl. Math. 26 (2001), 47 – 52.

J. Liu and B. Liu, On relation between energy and Laplacian energy, MATCH Commun. Math. Comput. Chem. 61 (2009), 403 – 406.

M.R. Rajesh Kanna and R. Jagadeesh, Minimum covering Randic energy of a graph, Advances in Linear Algebra and Matrix Theory 6 (2016), 116 – 131.

M. Randic, On characterization of molecular branching, J. Amer. Chem. Soc. 97 (1975), 6609 – 6615.

S. Radenkovic and I. Gutman, Total (pi)-electron energy and Laplacian energy: How far the analogy goes? J. Serb. Chem. Soc. 72 (2007), 1343 – 1350.

M. Robbiano and R. Jiménez, Applications of a theorem by Ky Fan in the theory of Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 62 (2009), 537 – 552.

D. Stevanovic, I. Stankovic and M. Miloševic, More on the relation between energy and Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 61 (2009), 395 – 401.

H. Wang and H. Hua, Note on Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 59 (2008), 373 – 380.

B. Zhou, On the sum of powers of the Laplacian eigenvalues of graphs, Lin. Algebra Appl. 429 (2008), 2239 – 2246.

B. Zhou, New upper bounds for Laplacian energy, MATCH Commun. Math. Comput. Chem. 62 (2009), 553 – 560.

B. Zhou, I. Gutman and T. Aleksic, A note on Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), 441 – 446.

B. Zhou and I. Gutman, On Laplacian energy of graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 211 – 220.

B. Zhou and I. Gutman, Nordhaus-Gaddum-type relations for the energy and Laplacian energy of graphs, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.) 134 (2007), 1 – 11.




DOI: http://dx.doi.org/10.26713%2Fcma.v9i2.533

Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905