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2.3 Planar Graphs. 🔗. Objectives. After completing this section, you should be able to do the following. Distinguish between planar and non-planar graphs. Use Euler’s formula to prove that certain graphs are non-planar. Apply Euler’s formula to polyhedra. 🔗. Section Preview. 🔗. Investigate!
Searches related to planar and non planar graph examples for kids math activities
- Properties of Planar Graphs
- Non-planar Graph
- Properties of non-planar Graphs
- Graph Coloring
- Applications of Graph Coloring
- State and Prove Handshaking Theorem.
If a connected planar graph G has e edges and r regions, then r ≤e.If a connected planar graph G has e edges, v vertices, and r regions, then v-e+r=2.If a connected planar graph G has e edges and v vertices, then 3v-e≥6.A complete graph Knis a planar if and only if n<5.A graph is said to be non planar if it cannot be drawn in a plane so that no edge cross. Example:The graphs shown in fig are non planar graphs. These graphs cannot be drawn in a plane so that no edges cross hence they are non-planar graphs.
A graph is non-planar if and only if it contains a subgraph homeomorphic to K5 or K3,3 Example1: Show that K5is non-planar. Solution: The complete graph K5contains 5 vertices and 10 edges. Now, for a connected planar graph 3v-e≥6. Hence, for K5, we have 3 x 5-10=5 (which does not satisfy property 3 because it must be greater than or equal to 6). Th...
Suppose that G= (V,E) is a graph with no multiple edges. A vertex coloring of G is an assignment of colors to the vertices of G such that adjacent vertices have different colors. A graph G is M-Colorable if there exists a coloring of G which uses M-Colors. Proper Coloring:A coloring is proper if any two adjacent vertices u and v have different colo...
Some applications of graph coloring include: 1. Register Allocation 2. Map Coloring 3. Bipartite Graph Checking 4. Mobile Radio Frequency Assignment 5. Making a time table, etc.
Handshaking Theorem:The sum of degrees of all the vertices in a graph G is equal to twice the number of edges in the graph. Mathematically it can be stated as: ∑v∈Vdeg(v)=2e Proof: Let G = (V, E) be a graph where V = {v1,v2, . . . . . . . . . .} be the set of vertices and E = {e1,e2. . . . . . . . . .} be the set of edges. We know that every edge l...
Apr 11, 2022 · An intuitive explanation of Kuratowski’s Theorem and Wagner’s Theorem, with lots of diagrams! A planar graph is one that can be drawn in a plane without any edges crossing. For example, the...
- Russell Lim
It seems that some graphs can be drawn without overlapping edges – these are called planar graphs – but others cannot. K 3 is planar. K 4 is planar is not planar .
Not all graphs are planar; for example, K5 and K3,3 are known to be non-planar graphs. The process of determining whether a graph is planar can be performed using techniques like Kuratowski's Theorem or the planarity testing algorithm.
A graph G is called planar if there is a way to draw G in the plane so that no two distinct edges of G cross each other. Let G be a planar graph (not necessarily simple).
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Figure 1.2: Planar, non-planar and dual graphs. (a) Plane ‘butterfly’graph. (b, c) Non-planar graphs. (d) The two red graphs are both dual to the blue graph but they are not isomorphic. Image source: wiki. Given a graph G,itsline graph or derivative L[G] is a graph such that (i) each vertex
