Author Type

Graduate Student

Date of Award

2014

Document Type

Dissertation

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Locke, Stephen C.

Abstract

This dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of application-oriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks and web graphs. In chapter 2, we study path systems, reduced path systems and how to construct a super edge-graceful tree with any number of edges using path systems. First, we give an algorithm to reduce a labeled path system to a smaller labeled path system of a different type. First, we investigate the cases (m, k) = (3; 5) and (m, k) = (4; 7), where m is the number of paths and 2k is the length of each path, and then we give a generalization for any k, m = 3 and m = 4. We also describe a procedure to construct a super-edge-graceful tree with any number of edges.

Extent

85 p.

Comments

Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2014.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.

Identifier

FA00004289

Format

pdf

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