Solve your IGNOU Doubts

Question:

Find a minimum-weigh spanning tree in the following graph

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Question:

Does there exist a 3-edge-colourable graph on 10 vertices and having 20 edges? Justify.

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Question:

There exists a complete binary tree on 15 vertices.

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Question:

The line graph of the Petersen graph has 30 edges.

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Question:

If κ(G) < κ0 (G), then δ(G) ≥ 4.

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Question:

The complement of a disconnected graph is connected.

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Question:

The vertex-covering number of an odd cycle is 1 more than its independence number.

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Question:

K₄, as a plane graph, is self-dual.

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Question:

Gr¨otzsch graph is Eulerian.

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Question:

For some nonnegative integers d₁, d₂, . . . , d_n the sequence (max{d₁, n}, d_2,d₃, . . . , d_n) is graphic.

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Question:

Every 2-connected bipartite graph is Hamiltonian.

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Question:

Every tree has a perfect matching.

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Question:

Construct a 4-directional and 8-directional chain code for the shape of the alphabet ‘C’. Hence, obtain its difference code and shape number.

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Question:

Two images g (x, y) 1 and g (x, y) 2 have histograms 1 hg and hg , 2 respectively. Give the condition under which the histograms of the following can be determined:

i) g₁ (x, y) g₂ (x, y)
ii) g₁ (x, y) g₂ (x, y)
iii) g₁ (x, y) g₂ (x, y)
iv) g₁ (x, y) g₂ (x, y)

Hence, obtain the histogram in each case in terms of hg1 and hg . 2

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Question:

Find the entropy of the image

$\begin{bmatrix} 0 & 1& 0 &0 \\ 0 & 1& 2& 2\\ 0 & 1& 2 &3 \\ 1& 2& 2& 3 \end{bmatrix}$

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Question:

Compute the degree of compression that can be achieved using (i) Huffman coding, and (ii) Run length coding, assuming two-bits to represent the pixel value and twobits to represent the run length.

$I=\begin{bmatrix} 3 & 3& 3 &2 \\ 2& 3& 3 & 3\\ 3 &2 & 2 &2 \\ 2 & 1& 1 &0 \end{bmatrix}$