Appendix

Summary

This appendix contains the following graph tables:

Table A1: Some graphs related to graphs with least eigenvalue —2

Table A2: The exceptional graphs with least eigenvalue greater than —2

Table A3: Regular exceptional graphs and their spectra

Table A4: A construction of the 68 connected regular graphs which are not line graphs but cospectral with line graphs

Table A5: One-vertex extensions of exceptional star complements

Table A6: The maximal exceptional graphs

Table A7: The index and vertex degrees of the maximal exceptional graphs.

Each table is accompanied by a description of its structure and content.

SOME GRAPHS RELATED TO GRAPHS WITH LEAST EIGENVALUE —2

Table A1 consists of two parts:

A1.1. Spectra of the Smith graphs and the reduced Smith graphs,

A1.2. Minimal graphs with least eigenvalue less than —2 on 7 and 8 vertices.

Spectra of the Smith graphs and the reduced Smith graphs

The Smith graphs are given in Fig. 3.2 and the reduced Smith graphs in Fig. 3.3 of Chapter 3. In both cases, the subscript in the name accorded to a graph denotes the number of vertices. We list the spectra of the Smith graphs and the reduced Smith graphs as given in [CvGu]. Each spectrum includes eigenvalues of the form 2 cos j for some m and j. For each graph in the table below we give m and the range of j together with any additional eigenvalues.