{"title":"Bounds on the Second Stage Spectral Radius of Graphs","authors":"S.K.Ayyaswamy, S.Balachandran, K.Kannan","volume":35,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":975,"pagesEnd":979,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/8804","abstract":"
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.<\/p>\r\n","references":"[1] R. Balakrishnan, The energy of graph, Linear Algebra Appl. 387(2004)\r\n287-295.\r\n[2] D.Cvetkovic, M. Doob, H. Saches, Spectra of Graphs- Theory and Application,\r\nthird ed., Johann Ambrosius Barth Verlag, Heidelberg, Leipzig,\r\n1995.\r\n[3] Dasong Cao, Bounds on Eigenvalues and Chromatic Numbers, Linear\r\nAlgebra and its Applications, 270 (1998), 1-13.\r\n[4] M.N.Ellingham and X.Zha, The spectral radius of graphs on surfaces,\r\nJ.Combin.Theory Series B 78(2000), 45-56.\r\n[5] D. Stevanovic, The largest eigenvalue of nonregular graphs,\r\nJ.Combin.Theory B 91(2004) 143-146.\r\n[6] Yuan Hong and Jin-Long Shu, A Sharp Upper Bound of the Spectral\r\nRadius of Graphs, Journal of Combinatorial Theory, Series B 81,177-\r\n183(2001).","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 35, 2009"}