Bounds on Energy and Laplacian Energy of Graphs

Sridhara G, Rajesh Kanna

Abstract


Let G be simple graph with n vertices and m edges. The energy E(G) of G, denotedby E(G), is dened to be the sum of the absolute values of the eigenvalues of G. Inthis paper, we present two new upper bounds for energy of a graph, one in terms ofm,n and another in terms of largest absolute eigenvalue and the smallest absoluteeigenvalue. The paper also contains upper bounds for Laplacian energy of graph.

Keywords


Adjacency matrix, Laplacian matrix, Energy of graph, Laplacian energy of graph.

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References


H.S Ramane, H.B walikar, Bounds for the eigenvalues of a graph,

Graphs,Combinatorics, algorithms and applications, Narosa publishing House, New Delhi,2005

D.Cvetkovic, I.Gutman (eds.),Applications of Graph Spectra (Mathematical Insti-tution,Belgrade,2009)

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

A. Yu, M. Lu, F. Tian, On spectral radius of graphs, Linear algebra and its applications, Vol.387, 41-49(2004)

A.Graovac, I.Gutman, 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 103,1-22 (1978)

T. AleksioLc, Upper bounds for Laplacian energy of graphs, MATCH Commun.Math. Comput. Chem, 60: 435-439,2008.

I.Gutman, in 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),pp. 196 - 211.

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

Huiqing Liu,Mei Lu and Feng Tian, Some upper bounds for the energy of graphs Journal of Mathematical Chemistry, Vol. 41, No.1, (2007).

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

B. Zhou, I. Gutman and T. Aleksi, A note on Laplacian energy of graphs,MATCH Commun. Math. Comput. Chem., 60:441-446, 2008.

B. Zhou, New upper bounds for Laplacian energy, MATCH Commun. Math.Comput. Chem., 62:553-560, 2009.




DOI: https://doi.org/10.22342/jims.23.2.316.

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