Date of Publication

9-2000

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Physical Sciences and Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Arlene A. Pascasio

Defense Panel Chair

Severino D. Diesto

Defense Panel Member

Blessilda P. Raposa
Erminda C. Fortes

Abstract/Summary

This thesis is an expository work taken from Sections 1-8 of the paper entitled Tight Distance-Regular Graphs by Aleksandar Jurisic, Jack Koolen, and Paul Terwilliger which will appear in the Journal of Algebraic Combinatorics. It focuses on the following result: Let T = (X, R) be a distance-regular graph with diameter d greater than or equal to 3 and eigenvalues k = Oo greater than O1 greater than ... greater than Od. Then the valency k, intersection numbers a1 and b1 satisfy (O1 + k over a1 + 1) (Od + k over a1 + 1) greater than or equal to -ka1b1 over (a1 + 1)2 T is said to be tight whenever T is nonbipartite, and the equality above holds. It also discusses characterizations of tight distance-regular graphs which involve intersection numbers and cosine sequences.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

TG03114

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

vii, , 78 numb. leaves, 28 cm.

Keywords

Distance geometry; Graphic methods; Eigenvalues; Jacobi method

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