The total influence number of a graph

The graph labeling problem that appears in graph theory has a fast development recently. This problem is an assignment of integers or rationals to the vertices or edges or both subject to certain conditions. There are many applications in the literature such as coding theory, astronomy, circuit design, data base management. Graph labeling is also very important major areas of computer science like data mining, cryptography, communication network etc. The total influence number that can be viewed as vertex labeling problems concerned with the sum of the labels is a new approach to the concept of graph labeling. Although many vertex labeling problems concerning with the sum of all of the labels study to minimize the sum, the total influence number has the aim of maximizing the sum. In this thesis, the total influence number of a graph is studied. We give some theorems about the total influence numbers of complement graphs and complementary prisms for specific graphs. Additionally, an algorithm based on Dijkstra algorithm for computing the total influence number of a graph is given.