Bounds on the Second Stage Spectral Radius of Graphs
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071578Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1007
 R. Balakrishnan, The energy of graph, Linear Algebra Appl. 387(2004) 287-295.
 D.Cvetkovic, M. Doob, H. Saches, Spectra of Graphs- Theory and Application, third ed., Johann Ambrosius Barth Verlag, Heidelberg, Leipzig, 1995.
 Dasong Cao, Bounds on Eigenvalues and Chromatic Numbers, Linear Algebra and its Applications, 270 (1998), 1-13.
 M.N.Ellingham and X.Zha, The spectral radius of graphs on surfaces, J.Combin.Theory Series B 78(2000), 45-56.
 D. Stevanovic, The largest eigenvalue of nonregular graphs, J.Combin.Theory B 91(2004) 143-146.
 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).