Award Date

1-1-2005

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Michelle Schultz

Number of Pages

48

Abstract

Let n ≥ 2 be a positive integer. For a sequence ( S0, S1, S 2,..Sn-1) of nonnegative integers we study the problem of whether there exists a graph there exists a graph containing i=0n-1Si vertices having exactly Si vertices whose degrees are congruent to i modulo n for each i = 0, 1, 2,.., n-1. When such a graph does exist, the sequence (S0, S 1, S2,..Sn -1) is said to be realizable. It is known for modulo 2, 3, and 4 that such a sequence is realizable with seventeen exceptions for modulo 3 and twenty-four exceptions for modulo 4. These results are known, but concise proofs of these facts have not appeared until this thesis; Further it had been conjectured that for each n ≥ 5 such sequences are realizable with finitely many exceptions. We show that there are finitely many exceptions for modulo 6 and further investigate how our proof technique might be generalized to the modulo 2n case.

Keywords

Certain; Concerning; Degrees; Existence; Graphs; Problem

Controlled Subject

Mathematics

File Format

pdf

File Size

1024 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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