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.
_______ ______ _______ _________ ______.
_________ ___ __________ _______ ______ _____ ________ ______ _______ _____ _______ _____.
__________ ________ ____ ________ ___ ________ _____.
________ _______ ___ _________ __________ ____ _________ ____.
_____ ________ ______ ______ _____ _________.
_____ _________ _____ ______ __________ ____ ___.
______ __________ ________ _____ ______.
___ _____ ______ _____ __________ _______ ______ ___ ________ ________ ______ ______.
____ ______ ______ _____ ___ ___ ____.
_____ ________ ___ ________ _________ ___ _____ _______ _________ _________ __________ _____.
______ _____ ____ _____ ______ _______ _________.
______ ______ _____ __________ _____ __________ _________ __________ _______ ________ _____ __________.
___ ______ _____ _______ _________ __________.
_______ __________ _____ _____ _____ _________ _________ ____ _______ ____.
___ _________ _______ ___ ________ ___ _____.
________ ______ _____ _________ _____ _____ ____ ____ ___ _____ __________.
__________ __________ ___ __________ ______ _________ __________ _________.
_______ ________ _____ ______ ___ _________ ____ ________.
______ _______ _______ ______ _____ ____ _______ _____ ______.
_______ _________ __________ ________ _________ ________.
__________ _______ ___ _____ _____ _________ _________ _____ _________ _______ __________.
______ ________.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
Make a table of the values of the Boolean function
f (x1;x2;x3) = x2(x1
x3)
Write the function in DNF using the table.
For the graph in Fig. Fig. 2 on the following page find a minimal colouring.
Find the number of ways of tying up 7 different books into 4 bundles if the order of the books in the bundles does not matter.
Show that any tree with exactly two vertices of degree 1 is a path.
Let A be an 88 Boolean matrix (i.e. every entry is 0 or 1). If the sum of the entries in A is 51, prove that there is a row i and a column j in A such that the entries in row i and in column j add up to more than 13. Further, show that there are at least 4 such pairs of rows and columns.
Write (x z)
(y
z') in CNF and DNF.
Find the generating function of the recurrence
an = 4an-1-4an-2+1
with initial conditions a0 = 1, a1 = 1.