#### Title

A disrespectful polynomial

#### Document Type

Article

#### Publication Date

1990

#### Publication Title

Linear Algebra and Its Applications

#### Department

Mathematics and Computer Science

#### Abstract

Given a graph and a polynomial, a matrix can be constructed by evaluating the polynomial with the adjacency matrix of the graph. When will the resulting matrix be the adjacency matrix of another graph? We answer this question for orbit polynomial graphs. We then investigate a conjecture of Weichsel relating the automorphism groups and eigenvalues of a graph *G* and another graph generated from *G* by a polynomial. For vertex-transitive graphs with a prime number of vertices the conjecture is true, but we also provide examples where it is false.

#### Volume

128

#### pp.

139-146

#### ISSN

0024-3795

#### WorldCat Link

#### Citation

Beezer, R. "A Disrespectful Polynomial." Linear Algebra and Its Applications. 128.1 (1990): 139-146. Print.