الفهرس | Only 14 pages are availabe for public view |
Abstract Graph theory has applications in many areas of computing, social and natural science. The theory is also intimately related to many branches of mathematics, including matrix theory, numerical analysis, probability, topology, and combinatory. A graph labeling is an assignment of integers to the vertices or edges or both, subject to certain conditions that have been motivated by practical problems, labeled graphs serve as useful mathematical models for a broad range of applications such as coding theory, including the design of good types codes, synch-set codes, missile guidance codes and convolutional codes with optimal autocorrelation properties. They facilitate the optimal nonstandard encodings of integer’s, labeled graph has also been applied in determining ambiguities in x-ray crystallographic analysis to design a communication network addressing system, database management in determining optimal circuit layouts and radio astronomy problems, etc. This thesis studies three types of radio numbering, namely radio mean number, radio mean square number and radio geometric mean number for paths and cycles. Moreover, it provides an algorithm that helps to find results with mathematical models to compare the values and result for any graphs. Also, this thesis introduces four different types of cordial labeling namely cordial, signed product cordial, Logical cordial and Total cordial, on the graphs (corona between path and second powers of lemniscate - corona between paths and kite - lemniscate - second powers of lemniscate - corona between path and cycles - kite -corona between cycles and kitecorona between paths and Third Power of Double Fans- corona between paths and Third Power of Generalize Fans- corona between paths and second power of Fan graphs). |