On highly irregular graphs

Date of Publication

2006

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Rigor B. Ponsones

Defense Panel Member

Anita C. Ong
Michele G. Tan

Abstract/Summary

This thesis is an exposition of the results discussed in two articles, namely, Highly Irregular graphs by Yousef Alavi, Gary Cahrtland, et al., published in Journal of Graph Theory, Volume II, No. 2, in 1987, and Highly Irregular Multitrees by Yousef Alavi, Don R. Lick, and Terry A. McKeet which appeared in graph Theory, Combinatorics, Algorithms and Applications in 1991. The thesis defines a highly irregular graph and discusses elementary properties of highly irregular graphs. It proves that every graph of order n 2 is an induced subgraph of a highly irregular graph. It also shows that the order n of a highly irregular tree with maximum degree d is at least 2. Furthermore, it proved that a multitree of maximum degree d and strength two is the unique highly irregular multitree of minimum possible order and minimum possible size.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU13513

Shelf Location

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

Physical Description

v, 54, [14] leaves : ill.

Keywords

Graph theory; Matrices; Combinatorial analysis

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