WUCT121 Discrete Mathematics Graphs Tutorial Exercises Solutions

(d) A graph with four vertices having the degrees of its vertices 1, 1, 2 and 2.
v 1
e 1
v 2
e 2
e 3
v 4
v 3
(e) A graph with four vertices having the degrees of its vertices 1, 1, 2 and 6.
v 1
e 1
v 2
e 2
v 4
e 3
v 3
e 4
e 5
(f) A graph with five edges having the degrees of its vertices 1, 1, 3 and 3.
Not possible, number of edges is 5, thus the sum of the degrees of the vertices
4
must be 2 × 5 = 10 ∑δ
( v i ) = 1+
1+
3 + 3 = 8 ≠ 2×
5
i=
1
WUCT121 Graphs: Tutorial Exercise Solutions 4