Bounds of Laplacian Energy of a Hypercube Graph
About this article
DOI:
https://doi.org/10.14419/ijet.v7i4.10.21287Keywords:
Hypercube graph, Laplacian Energy, Regular graphAbstract
Let Qn denote the n – dimensional hypercube with order 2n and size n2n-1. The Laplacian L is defined by L = D where D is the degree matrix and A is the adjacency matrix with zero diagonal entries. The Laplacian is a symmetric positive semidefinite. Let µ1 ≥ µ2 ≥ ....µn-1 ≥ µn = 0 be the eigen values of the Laplacian matrix. The Laplacian energy is defined as LE(G) = . In this paper, we defined Laplacian energy of a Hypercube graph and also attained the lower bounds.
References
Balakrishnan. R (2004), The energy of a graph, Linear Algebra and its applications, 287-295.
Bapat R. B , Pati S(2011), Energy of a graph is never an odd integer. Bull.Kerala Math. Assoc. 1, 129-132
Bo Zhou (2004), Energy of a graph, MATCH commu. Math. Chem. 51, 111-118.
Bo Zhou and Ivan Gutman (2007) , On Laplacian energy of a graph, Match commu. Math. Comput. Chem. 57, 211-220.
Bo Zhou (2010), More on Energy and Laplacian Energy Math. Commun. Math. Comput. Chem. 64, 75-84.
View more references (11)
Bo Zhou and Ivan Gutman (2006), On Laplacian energy of a graph, Linear algebra and its applications, 41, 429-37.
Cvetkovi’c .D, Doob M, Sachs H (1980), Spectra of graphs - Theory and applications, Academic Press, New York.
Gholam Hossein, Fath - Tabar and Ali Reza Asharfi (2010), Some remarks on Laplacian eigen values and Laplacian energy of graphs, Math. Commun., vol.15, No.2, 443-451.
Ivan Gutman, Emina Milovanovic, and Igor Milovanovic (2015), Bounds or Laplacian- Type graph energies, Math. Commun.,vol. 16 No. 1, 195-203.
Ivan Gutman(1978), The energy of a graph. Ber. Math – statist. Sekt. Forschungsz. Graz, 103, 1-22.
Juan Rada, Antonio Tinio (2004), Upper and Lower bounds for the energy of bipartite graph, Journal of Mathematics analysis and application, vol.289, 446-455.
Kinkar Ch. Das, Seyed Ahamed Mojallal, Ivan Gutman (2016) , On energy and Laplacian energy of bipartite graphs, Applied Mathematics and Computation 273, 759-766.
Merris .M (1994), Laplacian matrices of graphs, A survey, Lin. Algeba Appl. 143-176.
Nathan Reff (2011), New Bounds for the Laplacian Spectral Radius of a Signed graph, arXiv:1103, 4629VI[Math.Co], 21-23.
Stanley F. Florkowski I (2004), Spectral Graph theory of the Hypercube (Thesis).
Xiaogenchen, Wanwenxie (2012), Energy of hypercube and its complement, International Journal of Algebra, Vol 6, No.16, 799 – 805.