ON PROBLEMS OF CORDIALITY LABELING ON SOME GRAPHS

Abstract

The project in this thesis is based on the subject of graph theory, which studies graphs and operations on them. The thesis consists of four chapters: Chapter one :Basic concepts It is an introduction and presents the main definitions of graph theory and basic concepts of the cordial labeling applied for some graphs which are used in our project. Chapter two: The cordiality of the sum of the second power of paths and stars In the first section of this chapter, we reformulate previous results of the cordiality of the join between paths and cycles. Also, we studied the cordial labeling of the sum of two graphs one of them is a second power of path and the other graph is a star graph which is cordial for all n, m except for (n ,m) = (4,odd) and (n ,m) = (6 , odd) and (n ,m) = (2, odd) and (n ,m) = (3 ,1 ). The results of this chapter and the next chapter are accepted for publications in “UTILITAS MATHEMATICA publishing INC “ in Canada .

Chapter three: Cordiality of the union of the second power of paths and stars In chapter three, we studied the cordiality labeling of the union of two graphs the first one is a second power of path and the other graph is a star graph. We reached that P_n^2 UK_(1,m)is cordial for all n and m except (n , m)≠ (2, odd) . -vi-

Chapter four: The cordiality of the product of two graphs In this chapter , we studied the cordiality labeling of the Cartesian product of two graphs. The cordiality labeling of the product of some graphs has been studied and some theorems are obtained. We showed in the first section that the Cartesian product graphs P_(2s+i)×C_(2s+j) are cordial for i, j =0, 1 . In the second section, we discussed the cordiality of the graphs P_(2s+i)×P_(2s+j ). In the third section, The cordiality of C_(2s+i)×P_(2s+j) had been discussed. In the last section of this chapter, we showed some real applications based on graph labeling.