Research Questions and Objectives Flashcards
(5 cards)
What specific research questions or objectives are outlined in the statement of the problem?
What is the upper D-eccentric domination number ΓeD(G)\Gamma^D_e(G)ΓeD(G) for specific graphs such as:
Wheel graphs WnW_nWn,
Complete bipartite graphs Km,nK_{m,n}Km,n,
Arrow graphs AnA_nAn?
How do these values compare to:
The upper domination number Γ(G)\Gamma(G)Γ(G),
The eccentric domination number?
These questions aim to explore how the introduction of eccentricity into the domination framework alters the values and properties of dominating sets.
How did you formulate your S.O.P (Statement of the Problem)?
The S.O.P. was formulated by:
Identifying the gap in the literature regarding the upper D-eccentric domination number,
Recognizing the lack of exact values and characterizations for this parameter in known graph families,
Framing the research problem as a theoretical investigation to derive new bounds, constructions, and relationships involving this parameter.
What is the purpose of your research?
The purpose of this study is to:
Determine the upper D-eccentric domination number ΓeD(G)\Gamma^D_e(G)ΓeD(G) for selected graph classes,
Analyze the influence of eccentricity in domination,
Extend domination theory by introducing and evaluating a less-explored but significant variation.
What are the specific objectives of your study?
To define and formalize the upper D-eccentric domination number.
To compute or bound this parameter for wheel graphs, complete bipartite graphs, and arrow graphs.
To compare these values with classical domination and eccentric domination numbers.
To characterize upper D-eccentric dominating sets in the studied graphs.
To contribute original theoretical results that fill a gap in graph theory.
Are your objectives achievable within the scope and timeframe of your study?
Yes, the objectives are achievable because:
The study focuses on well-defined and structured graph classes,
The approach is theoretical, relying on logical deduction, established theorems, and constructive proofs,
The graphs chosen have manageable sizes and properties for closed-form analysis.
