[Discrete Mathematics] Planar Graphs. 65 просмотра 65 тыс. просмотров.  We look at planar graphs and how to determine if a graph is planar or not. Planar Graph in Graph Theory- A planar graph is a graph that can be drawn in a plane such that none of its edges cross each other. Planar Graph Example, Properties & Practice Problems are discussed.  Problem What is the maximum number of regions possible in a simple planar graph with 10 Planar Graph edges? Solution-. In a simple planar graph, degree of each region is >= 3. So, we have 3 x |R| <= 2 x |E|. In graph theory, a planar graph is a graph that can be embedded in the plane so that no edges intersect. For example, the following two graphs are planar: Error creating thumbnail: Unable to save thumbnail to destination. px. Note that second graph (the complete graph K4) can be redrawn without intersecting edges by moving one of the diagonal edges to the outside. On the other hand, the two graphs shown below are not planar.
Also Read-Bipartite Graph. PRACTICE PROBLEMS BASED ON PLANAR GRAPH IN GRAPH THEORY- Problem Let G be a connected planar simple graph with 25 vertices and 60 edges. Find the number of regions in G. Solution- Given-Number of vertices (v) = 25; Number of edges (e) = By Euler’s formula, we know r = e – v + 2. Substituting the values, we get-. Planar Graphs on Brilliant, the largest community of math and science problem solvers. Planar Graph Problems. Classical and recent results are surveyed in the development of efficient algorithms for the following eleven famous problems on planar graphs: planarity testing, embedding, drawing, separators, vertex-coloring, independent vertex set, listing subgraphs, Hamiltonian cycle, network flows, and Steiner trees and forests. Also typical methods and techniques useful for computational problems on planar graphs Cited by: 5.

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