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.