For the graph in Fig. Fig. 2 on the following page find a minimal colouring.
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Let fn denote the nth Fibonacci number. Show by induction that every natural number is expressible as a sum
fn1 + fn2 + .......+ fnk
where ni - ni+1 > 1 for each i > 1.
Is the graph in Fig. 1 Eulerian? Is it Hamiltonian? Justify your answers.
Which of the following sentences are statements? Give reasons for your answer.
i) Are the buses running today?
ii) What a pleasant weather!
iii) x2 +1 = 0 for a real value of x.
iv) Every odd number is a prime.
If an apple costsRs.15, a papaya costs Rs.17 and a banana costs Rs.8, write the generating function for the number of ways of purchasing these fruits with Rs.n.
Show that any tree with exactly two vertices of degree 1 is a path.
How many numbers from 0 to 999(0 and 999 inclusive) are not divisible by 5 or 13?
If a planar graph has the degree sequence {2;2;3;3;4;4;4}, how many faces will it have? Draw a planar graph with this degree sequence and number the faces to check your answer.