13. Show by example that the statement "every planar graph has a vertex with degree less than or equal to 4" is false.

Q: can you please provide explanations

A: Possible: Graph with 5: 3 vertices of degree 2 and 2 vertices of degree 1. Impossible: Graph with 5:…

Q: Sketch an undirected graph with the following vertex degrees 3,3,3,2,1 if it exists

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Q: 3. Determine the edge connectivity and the vertex connectivity of the following graph. Explain.

A: The vertex connectivity is the minimum number of vertex required to remove from graph to make graph…

Q: Define a pseudo graph?

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Q: Show that in every simple graph there is a path from every vertex of odd degree to some other vertex…

A: we have to prove that In every simple graph there is a path from every vertex of odd degree to some…

Q: Among each pair of the CEOs of N companies there is (a) mutual like; (b) mutual dislike; (c) neutral…

A:

Q: Determine all bipartite graphs G whose complement G is also bipartite.

A: Let G be bipartite, with bipartitions: B1 and B2. Then any three vertices in B1 will form a triangle…

Q: Show that every simple finite graph has two vertices of the same degree.

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Q: 3. Show that the following graph is planar: Without changing the vertex-set, what is the maximum…

A:

Q: A) Draw graph G with vertex set V (G) = {V₁, V2, V3, V4, V5, V6, V7} and edge set E (G) = {V₁V4, V₁…

A:

Q: We say that two distinct edges in a graph are adjacent if there is a vertex incident to both (the…

A: Solution

Q: The Euler's formula v - e + f = 2 holds for all connected planar graphs. What if the graph is not…

A: The formula for multiple connected component c is, v +f = e + c + 1

Q: (10) A graph is connected if, and only if, (Choose one answer from below) A) It consists of a few…

A: A connected graph is graph that is connected in the sense of a topological space, i.e., there is a…

Q: shortest path to any other vertex?

A:

Q: Can a simple graph exist with 9 vertices all of degree 5?

A: Handshaking lemma: In any graph, sum of degree of all the vertices is twice the number of edges…

Q: Complete a path straight at vertex a that ends at vertex c.

A: A complete path is defined when all the vertices are passed through and none of the smaller paths…

Q: Is it possible to have a graph that only has the form of a "simple graph"? Like it will not have a…

A: A simple graph is a graph having no loops or parallel edges. It also do not posses any directions…