Determinant and Pseudo-Determinant of Adjacency Matrices of Derived Graphs

  IJCTT-book-cover
 
International Journal of Computer Trends and Technology (IJCTT)          
 
© 2016 by IJCTT Journal
Volume-38 Number-2
Year of Publication : 2016
Authors : Rajendra P., R. Rangarajan
  10.14445/22312803/IJCTT-V38P115

MLA

Rajendra P., R. Rangarajan "Determinant and Pseudo-Determinant of Adjacency Matrices of Derived Graphs". International Journal of Computer Trends and Technology (IJCTT) V38(2):81-86, August 2016. ISSN:2231-2803. www.ijcttjournal.org. Published by Seventh Sense Research Group.

Abstract -
The determinant is the product of eigenvalues of adjacency matrix of a graph and pseudo-determinant is the product of non-zero eigenvalues of adjacency matrix of a graph. In this paper, we have computed determinant, pseudo-determinant, characteristic polynomial, spectrum, spread, separator and energy of derived graph of some standard graphs.

References
[1] C. Adiga, A. Bayad, I. Gutman and Shrikanth A. S., The minimum covering energy of a graph, Kragujevac J. Sci., 34 (2012), 39-56.
[2] Alireza Abdollahi, Determinants of adjacency matrices of graphs, Transactions on Combinatorics, 1(4) (2012), 9-16.
[3] S. K. Ayyaswamy, S. Balachandran and I. Gutman, On secondstage spectrum and energy of a graph, Kragujevac J. Sci., 34 (2010), 139-146.
[4] D. M. Cvetkovi´c, M. Doob and H. Sachs, Spectra of Graphs, Theory and Application, Academic Press, New York, USA(1980).
[5] W. X. Hong and L. H. You, On the eigenvalues of firefly graph, Transactions on Combinatorics, 3 (3)(2014), 1-9.
[6] http://mathworld.wolfram.com/TadpoleGraph.html.
[7] R. Rangarajan and P. Rajendra, Computation of spectral parameters of graphs, ifrsa International Journal of Computing, 4(4)(2014), 838-849.
[8] Xueliang Li, Yongtang Shi and I. Gutman, Graph Energy, Springer New York, 2012.

Keywords
Derived graph, Determinant, Pseudo-determinant, Spread and Separator.