Article ID Journal Published Year Pages File Type
4602395 Linear Algebra and its Applications 2008 12 Pages PDF
Abstract

In this paper we determine the graphs which have the minimal spectral radius (i.e., the largest eigenvalue of its corresponding adjacency matrix) among all the graphs of order n with the diameter D=n-4. This result settles a problem proposed in [E.R. van Dam, R.E. Kooij, The minimal spectral radius of graphs with a given diameter, Linear Algebra Appl. 423 (2007) 408–419], which is also the special case D=n-4 of the Conjecture 8 in van Dam and Kooij (2007).

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory