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an-3an-1-4an-2=4.3n


Use breadth-first search to produce a spanning tree for

each of the simple graphs in Exercises 1 3-15. Choose

a as the root of each spanning tree. 


Let A = {1,2,3,4,6,8,9,12,18,24} be a non-empty set and R be the partial order relation of

divisibility defined on A, i.e., If (a,b) ε A, then a divides b

i. Draw the Hasse diagram of R.

ii. Find the Maximal and Minimal elements in A

Let g be a function from Z+ (the set of positive integers) to Q (the set of rational numbers) defined by (x, y) element of g iff y = (g is a subset of Z+ mapped with Q) and let f be a function on Z + defined by (x, y) element of f iff y = 5x2 + 2x – 3 (f subset of Z+ mapped with Z+)

Which one of the following statements regarding the function g is TRUE? 

(Remember, g is a subset of Z+ mapped with Q.)

1. g can be presented as a straight line graph.

2. g is injective.

3. g is surjective.

4. g is bijective.



(a) Show that a simple connected graph with 7 vertices each of degree 4 is non-planar

(b) Find χ(Kn) & χ(Cn)


(a) In how many ways can a committee of 3 faculty members and two students be selected from 7 faculty members and 8 students

(b) How many ways are there to distribute 12 different books among 15 people if no person is to receive more than one book 


 Design a single error correcting code for m=3 & n=7


Show that ¬ (P"\\iff"Q)"\\iff"(P V Q) Λ ¬(P Λ Q) "\\iff"(P Λ ¬Q) V (¬ P Λ Q) without using truth table


There are 18 mathematics majors and 325 computer science majors at a
college.
a) In how many ways can two representatives be picked so that one is a
mathematics major and the other is a computer science major?

Find the generating function of recurrence relation an+1_an=3n ,n less than 0 where ao=1


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