Bounds on the Second Stage Spectral Radius of Graphs
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32912
Bounds on the Second Stage Spectral Radius of Graphs

Authors: S.K.Ayyaswamy, S.Balachandran, K.Kannan


Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

Keywords: Second stage spectral radius, Irreducible matrix, Derived graph

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1284


[1] R. Balakrishnan, The energy of graph, Linear Algebra Appl. 387(2004) 287-295.
[2] D.Cvetkovic, M. Doob, H. Saches, Spectra of Graphs- Theory and Application, third ed., Johann Ambrosius Barth Verlag, Heidelberg, Leipzig, 1995.
[3] Dasong Cao, Bounds on Eigenvalues and Chromatic Numbers, Linear Algebra and its Applications, 270 (1998), 1-13.
[4] M.N.Ellingham and X.Zha, The spectral radius of graphs on surfaces, J.Combin.Theory Series B 78(2000), 45-56.
[5] D. Stevanovic, The largest eigenvalue of nonregular graphs, J.Combin.Theory B 91(2004) 143-146.
[6] Yuan Hong and Jin-Long Shu, A Sharp Upper Bound of the Spectral Radius of Graphs, Journal of Combinatorial Theory, Series B 81,177- 183(2001).