Analysis of the k-Fibonacci numbers on graphs

Graph Theory is a useful area of applied mathematics. Graph Theory primarily helps to express, organize and solve the problem for which the solution is sought or the work for which the solution is sought, in the most effective way. Therefore, real problems are transformed into a graph structure, and it helps to find the most practical and economical solution to eliminate the problem. In this study, the definitions of Graph Theory and k-Fibonacci number are given, the properties of the k-Fibonacci number on the graph are examined. The thesis consists of 5 main parts. In the first chapter, basic concepts of graph theory, some special graphs and basic information about Omega invariant are given. In the second part, a literature review on Graf and k-Fibonacci numbers was made. In the third chapter, definitions, identities and theorems of Fibonacci, k-Fibonacci and Pell numbers are given. In the fourth chapter, the definition and theorems of the k-Fibonacci graph are given. Some parameters were obtained and their applications were made. In the fifth chapter, the results and recommendations are presented.