Hye Jin Jang, Jack Koolen, Akihiro Munemasa, Tetsuji Taniguchi

Ars Mathematica Contemporanea 7(1) 105-121 Jan 2014 [Refereed]

We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice....

Ars Mathematica Contemporanea 7(1) 247-262 Jan 2014 [Refereed]

In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least 1-τ, where τ is the golden ratio, can be described by a finite set of fat (-1 - τ )-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean th...

Ars Mathematica Contemporanea 5(2) 243-258 Jun 2012 [Refereed]

This is a continuation of the article with the same title. In this paper, the family H is the same as in the previous paper [11]. The main result is that a minimal graph which is not an H-line graph, is just isomorphic to one of the 38 graphs foun...

Linear Algebra and its Applications 435 2544-2559 Nov 2011 [Refereed]

In this paper, we classify the connected non-bipartite integral graphs with spectral radius three.

On graphs with the smallest eigenvalue at least , part I

T. Taniguchi

ARS MATHEMATICA CONTEMPORANEA 1(1) 81-98 Aug 2008 [Refereed]

There are many results on graphs with the smallest eigenvalue at least .
As a next step, A. J. Hoffman proposed to study graphs with the smallest eigenvalue at least . In order to deal with such graphs, R. Woo and A. Neumaier intr...

The smallest eigenvalues of the line graphs of some trees -- Cvetković and Stevanović's Question --

Gary Greaves, Jack Koolen, Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

Sep 2013

We give a structural classification of edge-signed graphs with smallest
eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest
eigenvalue of the line graph of a tree that was stated in the 1970s.
Furthermore, we prove a mo...