A planar graph is a type of graph in graph theory that can be drawn on a flat surface without any edges crossing. This means that the edges of the graph do not intersect each other.
A planar graph can be drawn on a flat surface without edges crossing, while a non-planar graph cannot be drawn without edges crossing. In other words, a non-planar graph has at least one set of edges that intersect each other.
Planar graphs have various practical applications, such as in network design and layout, circuit design, map coloring, and scheduling problems. They are also used in computer algorithms and data structures for solving various problems efficiently.
Yes, a planar graph can have negative edge weights. The weights of the edges in a planar graph do not affect its planarity, as long as the edges do not intersect when drawn on a flat surface.
There are several methods for determining if a graph is planar, including the Kuratowski's and Wagner's theorems, the Euler's formula, and the planar embedding algorithm. These methods involve checking for specific characteristics and properties of the graph, such as the number of edges, vertices, and faces, and the presence of subgraphs.