Date of Publication

2003

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Arlene A. Pascasio

Defense Panel Chair

Severino D. Diesto

Defense Panel Member

Isagani B. Jos
Erminda C. Fortes

Abstract/Summary

This thesis is an exposition of the article The Girth of a Thin Distance-regular Graph by Benjamin V.C. Collins, which was published in the Journal of Graphs and Combinatorics (1997) [3]. Let t denote a distance-regular graph with vertex set X, diameter D greater than or equal to 3, and valency k greater than or equal to 3. For a fixed vertex x E X, let T(x) denote the Terwilliger algebra of t with respect to x. An irreducible T(x)-module W is thin if dim E*iW less than or equal to 1 (0 less than or equal to i less than or equal to D), where E*i(x) is the ith dual idempotent of t with respect to x. The graph t is called thin if every irreducible T(x)-module is thin with respect to every vertex x E X. Moreover, a regular generalized quadrangle is a bipartite distance-regular graph with girth 8 and diameter D = 4. The main results of [3] that are explained in detail in this thesis are as follows: t is a regular generalized quadrangle if and only if t is thin and the intersection number c3 = 1. Moreover, if t is thin then the girth is 3, 4, 6 or 8. The girth is exactly 8 when t is a regular generalized quadrangle.

Abstract Format

html

Note

Title from title screen.

Language

English

Format

Electronic

Accession Number

CDTG003556

Shelf Location

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

Keywords

Graph theory; Combinatorial analysis

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