Lower Bounds for Energy of Matrices and Energy of Regular Graphs


Download PDF

Authors: M. R. OBOUDI

DOI: 10.46793/KgJMat2205.701O

Abstract:



Keywords:

Energy of matrices, energy of graphs, energy of regular graphs.



References:

[1]   S. Akbari, E. Ghorbani and M. R. Oboudi, Edge addition, singular values, and energy of graphs and matrices, Linear Algebra Appl. 430 (2009), 2192–2199.

[2]   A. E. Brouwer and W. H. Haemers, Spectra of Graphs, Springer, New York, 2012.

[3]   D. Cvetković, P. Rowlinson and S. Simić, An Introduction to the Theory of Graph Spectra, London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 2010.

[4]   I. Gutman, On graphs whose energy exceeds the number of vertices, Linear Algebra Appl. 429 (2008), 2670–2677.

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

[6]   I. Gutman, S. Zare Firoozabadi, J. A. de la Peña and J. Rada, On the energy of regular graphs, MATCH Commun. Math. Comput. Chem. 57(2) (2007), 435–442.

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

[8]   R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985.

[9]   V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326(2) (2007), 1472–1475.

[10]   M. R. Oboudi, Bipartite graphs with at most six non-zero eigenvalues, Ars Math. Contemp. 11(2) (2016), 315–325.

[11]   M. R. Oboudi, Cospectrality of complete bipartite graphs, Linear Multilinear Algebra 64(12) (2016), 2491–2497.

[12]   M. R. Oboudi, Energy and Seidel energy of graphs, MATCH Commun. Math. Comput. Chem. 75(2) (2016), 291–303.

[13]   M. R. Oboudi, On the third largest eigenvalue of graphs, Linear Algebra Appl. 503 (2016), 164–179.

[14]   M. R. Oboudi, On the difference between the spectral radius and maximum degree of graphs, Algebra Discrete Math. 24(2) (2017), 302–307.

[15]   M. R. Oboudi, Characterization of graphs with exactly two non-negative eigenvalues, Ars Math. Contemp. 12(2) (2017), 271–286.

[16]   M. R. Oboudi, Majorization and the spectral radius of starlike trees, J. Comb. Optim. 36(1) (2018), 121–129.

[17]   M. R. Oboudi, On the eigenvalues and spectral radius of starlike trees, Aequationes Math. 92(4) (2018), 683–694.

[18]   M. R. Oboudi, Distance spectral radius of complete multipartite graphs and majorization, Linear Algebra Appl. 583 (2019), 134–145.

[19]   M. R. Oboudi, A new lower bound for the energy of graphs, Linear Algebra Appl. 580 (2019), 384–395.

[20]   M. R. Oboudi, A relation between the signless Laplacian spectral radius of complete multipartite graphs and majorization, Linear Algebra Appl. 565 (2019), 225–238.