17

18 a)
b)

19 a
b

20 a)
b)

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(1)

Apply Dijkstra’s algorithm to find shortest path in the given graph starting with (10)

vertex ‘0’ as source.

Find at-least 6 circuits for the given graph and generate the corresponding (7)

circuit matrix representation with the circuits obtained. (Note: Assume suitable

names for the vertices and edges.)

State the different properties of a path matrix representation of a graph. (3)

Prove that the rank of an incidence matrix of a connected graph with 1 vertices (4)

is 1-1.

Describe the steps invloved in the Prim’s algorithm for computing the (6)

minimum spanning tree of a given graph.

Prove the statement, “If By is a fundamental circuit matrix of a connected graph (4)

G with € edges and n vertices, rank of Bs=e —n+ 1.”

With an example state how a cut-set matrix of a graph is generated. Also state (6)

the different properties of the cut-set matrix representation.

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