Question

File Edit Format View Help Graphs and trees 4. [6 marks] Using the following graph representation (G(V,E,w)): v a,b,c,d,e,f E fa,b), (a,f),fa,d), (b,e), (b,d), (c,f),(c,d),(d,e),d,f)) W(a,b) 4,W(a,f) 9,W(a,d) 10 W(b,e) 12,W(b,d) 7,W(c,d) 3 a) Draw the graph including weights. b) Given the following algorithm for Inding a minimum spanning tree for a graph: Given a graph (G(V,E)) create a new graph (F) with nodes (V) and no edges Add all the edges (E) to a set S and order them by weight starting with the minimum weight While S is not empty and all the nodes V in F are not connected: Remove the edge s from set S with the lowest weight If it does not cause a cycle to form, keep it Else discard it from F Using your graph from a) as G, i. Provide the order of the edges as they are removed from S, and note whether it is kept or discarded. ii. Draw the resulting spanning tree F. 5. Determine whether the following graph contains Eulerian and Hamiltonian cycles (and provide an example of an Eulerian/Hamiltonian cycle if so; do not provide all cycles) and explain brie2y how you found them. V (a,b,c,d,e,f,g,h,i)

Answer 1

SOLUTION:

ANSWER TO 5TH QUESTION:

DEFINITIONS:

WALK:

No edge appears more than once in a walk, a vertex however may appear more than once.

CLOSE WALK:

when a walk begins and ends at the same vertex is called closed walk.

PATH:

A open walk in which no vertex appears more than once is called path.

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SOLUTION TO 4TH QUESTION:

sa, b, c, d,e,s V w (e)-

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NOTE:

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