Polynomials of the Adjacency Matrix of a Graph (distance-Transitive, Distance-Regular, Orbit)

Given graphs (GAMMA) and (DELTA), and a real polynomial r(x), we will say that (DELTA) is generated from (GAMMA) by r(x) if r(A((GAMMA))) = A((DELTA)) where A((GAMMA)) and A((DELTA)) are adjacency matrices. For several interesting classes of graphs it is possible to determine all of the graphs which can be generated by a polynomial. Define the ith distance graph, (GAMMA)(,i), as the graph with the same vertex set as (GAMMA) and two vertices are adjacent in (GAMMA)(,i) if and only if they are a distance i apart. If (GAMMA) is a distance-regular graph, then for each i there exists a polynomial of degree i, p(,i)(x), such that p(,i)(A((GAMMA))) = A((GAMMA)(,i)). In fact, it has been shown that this property characterizes distance-regular graphs.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Beezer, Robert Arnold

• Mathematics

Identifier

(UMI)AAI8422017

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71218