SOME CONTRIBUTIONS TO HUB PARAMETERS OF GRAPHS - A THESIS - Master Degree in Mathematics

Aug 21, 2026

A formal master’s thesis in mathematics investigates hub parameters defined for graphs, developing theory around the “hop hub number,” “hop hub-integrity,” and related concepts. The study introduces foundational definitions and terminology, presents background context, and outlines research objectives and methodology before deriving new results. Additional contributions establish results for splitting graphs and introduce the “hop hubtic number” and “hop hub polynomial,” including relationships for standard graphs.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages107

Reading Time4 h 30 min

AccessFree to download

Introduction

Basic definitions and terminologies of a graph

Background of the study

Research Objectives

Methodology

Short outline of the thesis

Hop hub number of graphs

Introduction

The hop hub number of graphs

Hop hub number of line graphs

Hop hub-integrity of graphs

Introduction

The hop hub-integrity of graphs

Some properties of hop hub-integrity of line graphs

New results on hop hub number and hop hub-integrity of splitting graph

Introduction

The hop hub number of splitting graph

The hop hub-integrity of splitting graph

Hop hubtic number and hop hub polynomial of graphs

Introduction

The hop hubtic number of graphs

Hop hub polynomial of graphs

Hop hub polynomial of standard graphs

SOME CONTRIBUTIONS TO HUB PARAMETERS OF GRAPHS A THESIS SUBMITTED AS PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE MASTER DEGREE IN MATHEMATICS AL-BAYDHA University (Department of Mathematics) BY Abdu-Alkaﬁ Saead Qaid Sanad UNDER THE GUIDANCE OF Dr. Sultan Senan Mahde Faculty of Education and Science-Rada'a Al-Baydha University Al-Baydha, Yemen March, 2022 DEDICATED This Thesis is lovingly dedicated to the dearest people of my heart To the first teacher in life, source of all that is important tome, for Muhamad is messenger of god. To my first love, my mother. for years of unwavering support and guidance my beloved father. To the pure soul of my brother, the martyr muhamad. To my beloved, sisters and brothers. To my love and happiness, To my wife. To every piece of my soul, my children. To the best teacher in my life, source of my strengths, To the secret of my strength in life, all my friends. To the secret of my success all, my students. To all of them I say, I love you so much. CERTIFICATE This is to certify that the thesis "SOME CONTRIBUTIONS TO HUB PARAMETERS OF GRAPHS" is the result of research work done by Mr Abdu-Alkafi Saead Qaid Sanad under my supervision. The thesis has been the outcome of the original investigation in his area of research for a period for a year. The thesis as a whole or any part of it has not been submitted in part or in full to any other institution for the award of any other degree/diploma/associate ship/fellowship. Signature of the Research Supervisor and Date (Dr. Sultan Senan Mahde) Acknowledgments Praise is to Allah, Lord of the Heavens, the Earth, who gave me the potential and ability to complete this thesis. First of all, I would like to express my sincere gratitude to my Guide Dr. Sultan Senan Mahde, Assistant Professor, Department of Mathematics, Radaa - Al-Baydha University, for all the assistance he provided me, and for the guidance, and continuous encouragement greatly in reaching the end of this thesis. I have expended energy in shaping my research competence, politically reviewing my work and making valuable suggestions. And all the basic information from beginning to end is all thanks, appreciation and respect. Secondly, I would like to thank every doctor who taught me or contributed to my teaching from university doctors in the introductory stage, especially Prof. Dr. Abdullah Al-Sherai. I also extend my full appreciation and thanks to the doctors and their support and encouragement to ﬁnish this work, and also thanks to the University Administration represented by the President of the University, Prof. Ahmed Al-Arami, for his eﬀective contribution to the success and approval of the program. I also thank my colleagues at work for providing all the support and continuous encouragement and solving all the diﬃculties I face. My special thanks and appreciation to my beloved wife, Mrs. A. Al- Hanomi, for her constant care and support. She has always made me feel that"I could do anything that I want to achieve", and my lovely daughter malakand my son omar, whose natural smile and compassion always extended tome the real relief. Finally, my ineﬀable gratitude goes to my whole family, my parents, wife, children, brothers and sisters for all their love, support and patience. Without their support and encouragement, I cannot concentrate on my work and overcome the diﬃculties. Abdu-Alkafi Saead Qaid Sanad Table of Contents Table of Contents v 1 Introduction xiii 1.1 Introduction ................................ 1 1.2 Basic deﬁnitions and terminologies of a graph ............. 4 1.3 Background of the study ......................... 19 1.4 Research Objectives ........................... 22 1.5 Methodology ............................... 23 1.6 Short outline of the thesis ........................ 24 2 Hop hub number of graphs 26 2.1 Introduction ...........................

FAQs

What mathematical objects does the thesis study?

The thesis studies graphs and specific hub parameters defined on them, including hop hub number and hop hub-integrity.

What are the main research components covered?

It covers introductions and basic graph definitions, then develops results for hop hub number, hop hub-integrity, and new findings for splitting graphs.

What additional hub-related quantities are introduced or analyzed?

The thesis introduces the hop hubtic number and studies hop hub polynomials of graphs and standard graphs.

Aug 21, 2026

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