Fractional graph theory is a branch of graph theory that deals with fractional versions of classical graph theory concepts. The main idea is to generalize the concept of integral graph theory by introducing fractional weights to edges and vertices of a graph.
In fractional graph theory, the focus is on studying various graph parameters and problems, such as graph coloring, edge coloring, and the maximum flow problem, but in the context of fractional values. This means that instead of looking for integral solutions, we look for solutions that involve fractional values.
For example, in the context of graph coloring, we can assign a fractional weight to each vertex instead of assigning an integer value to each vertex. Similarly, in the maximum flow problem, we can assign fractional weights to edges instead of integral capacities.
Fractional graph theory has several applications in computer science, operations research, and engineering. It is used in the design and analysis of algorithms, network optimization, and communication networks, among other areas.
