Home
Add
Get on Google Play
Home
> Edit
Add/Update Thesis
Title*
Author's Name*
Supervisor's Name
Abstract
In this thesis a new graph invariant, cycle discrepancy, is introduced. The optimal bounds on the cycle discrepancy for class of three-regular graphs and class of 3-colorable graphs are found. If the class of three-regular graphs is further restricted to Halin graphs, the established bound on cycle discrepancy reduces linearly. Necessary and sufficient conditions are given for a graph to have maximum possible cycle discrepancy. Further, it is shown that computing cycle discrepancy of a graph is an NP-hard problem. Let G = (V,E) be an undirected simple graph on n vertices. The cycle discrepancy of G, denoted as cycdisc(G) is in general bounded as: 0 ≤ cycdisc(G) ≤ ⌈n 2 ⌉. If G is a three colorable graph then cycdisc(G) is tightly bounded by ⌊n 3 ⌋. For d > 3, such d-colorable graphs are presented that have maximum possible cycle discrepancy. If G is a cubic graph then there is a tight bound of n+2 6 on its cycle discrepancy. An O(n2) algorithm is also presented to label the vertices of G such that cycdisc(G) ≤ n+2 6 . If G is not only cubic but also a Halin graph then cycdisc(G) ≤ n 8 +O(log n) and this bound is tight apart from the additive O(log n) term. It is also established that if minimum-degree of G is 3n 4 then cycdisc(G) = ⌈n 2 ⌉. Further, for n > 6, if maximum-degree of G is Δ and Δ2 < n − 1, then cycdisc(G) < ⌈n 2 ⌉. A graph is also constructed with maximum-degree n 2 + 2, that has maximum possible cycle discrepancy. This thesis provides a ground for further investigation in this area.
Subject/Specialization
Language
Program
Faculty/Department's Name
Institute Name
Univeristy Type
Public
Private
Campus (if any)
Institute Affiliation Inforamtion (if any)
City where institute is located
Province
Country
Degree Starting Year
Degree Completion Year
Year of Viva Voce Exam
Thesis Completion Year
Thesis Status
Completed
Incomplete
Number of Pages
Urdu Keywords
English Keywords
Link
Select Category
Religious Studies
Social Sciences & Humanities
Science
Technology
Any other inforamtion you want to share such as Table of Contents, Conclusion.
Your email address*