Problem 3 Let Kn be the graph on n vertices such that every pair of two vertices are connected by an edge. Let u and u be two vertices of Kn. (a) How many walks of length 3 are there from u to v?

Q: Write down a path in the following graph from v₁ to v7 that uses exactly seven edges. 5 V1 V2 d f a…

A: we have given a graph with edges and its points given as follows:

Q: Find the edge chromatic number of Kₙ when n is a positive integer.

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Q: Graph G is defined by the arrow diagram below. 1 2 4 Select the pair of vertices such that there is…

A: Given that -

Q: Show that if n > R(6,6) and we partition the edges of the complete to 4 pieces then one of the…

A: According to the given information, it is required to show that:

Q: 0 D The diagram below shows a directed graph. Answer the following 5 questions based on this…

A: In the given digraph, there are two incoming edges to the vertex d and those are c→d, c→f and c→g.…

Q: Would a segment need to be drawn between v7 & v12? Those vertices don't appear to be of degree 5.

A: We have to determine whether we need to draw an extra edge between the vertices v7 and v12.Clearly…

Q: Question 1.9. Let Kn:r denote the Kneser graph, whose vertex set is the set of r-element subsets of…

A: GivenLet  denote the Kneser graph, whose vertex set is the set of element subsets of an element…

Q: Find the edge chromatic number of Kn when n is positive integer.

A: We have to find the edge chromatic number of  when  is positive integer.

Q: Question 4 Note that if (j, k) and (m, n) are pairs of integers then we can add them in a natural…

A: A vertex set is the set of all vertices of the graph. There are two points in the  vertex set which…

Q: Bo E

A: Walk:        Let G be graph, then the walk between the vertices v0 to vk is a sequence of…

Q: A cycle in a simple graph is a closed walk of length greater than m. What is the value of m?

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Q: How many Euler paths are there in this graph?

A: The objective is to find the Euler path in the graph

Q: E D

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Q: 5 (i)

A: Answer for  sub question a: Given graph is, G=V,E,V=a,b,c,d,e, E=∅ 1) Note: A vertex with no…

Q: 5. What happens to the graph of y = ax² + bx + c when: (note that parts A-E involve more than one…

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Q: 5) PER CLASS DISCUSSIONS IS THERE AN EULER CIRCUIT IN THE GRAPH?? Y OR N

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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: Draw diagrams for grid graphs Gm,n that is D(Gm,n) for all Gm,n with m≤ 7 and n ≤ 7 including…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

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: If u and v are vertices of a connected graph G, then d(u, v) is the length of a shortest path in G…

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Q: If OA, OB and OC are three edges of a parallelepiped where O is (0,0,0), A is (5,9,-3), Bis (2,-1,5)…

A: To find the coordinates of the other four vertices (D, E, F, and G) of the parallelepiped, we can…