الفهرس | Only 14 pages are availabe for public view |
Abstract This thesis consists of five chapters. Chapter one: In chapter one we introduce some basic definitions and theorems in number theory and graph theory which we need afterwards. Chapter two: In chapter two, we study some necessary conditions for a graph to be adivisor graph. Also, we study the dependance of these conditions pairwisely. And finally we prove that they are altogether not sufficient for a graph to be a non-divisor graph. Chapter three: In chapter three, we study some necessary conditions for a graph to be strongly multiplicative. Also, we study the dependence of these conditions pair-wisely. And finally we prove that they are altogether notsufficient for a graph to be a non-strongly multiplicative graph. Chapter four: In chapter four, we study some necessary conditions for a graph to be a strongly *-graph. Also, we study the dependence of these conditions pair-wisely. And finally we prove that they are altogether not sufficient for a graph to be a non-strongly *-graph. Chapter five: In chapter five, we study some necessary conditions for a graph to be apermutation graph. Also, we study the dependence of these conditions pair-wisely. And finally we prove that they are altogether not sufficient for a graph to be a non-permutation graph. This thesis contains five papers: 1- The results of Chapter 2 appeared in the journal The Egyptian Mathematical Society Vol. 18(2) 2010. 2- The results of Chapter 3 will appear in the international Canadian journal Ars Combinatoria. 3- Some results of chapter 4 will appear in AKCE International Journal of Graphs and Combinatorics. 4- The results of Chapter 5 will appear in the journal The Egyptian Mathematical Society. 5- Some results of chapter 4 are submitted for publication and still under refereeing |