Key for homework 3
Problem 37. Proposition. If G is of order p ( 2) and every vertex v of G has deg v
(p 1)/2, then G is connected.
Proof. (by contradiction) Let us assume that G is disconnected. Then G has k components
(k 2). Let ui denote an arbitrary
Key for homework 2
2.2 The degree sequence 2, 3, 3, 4, 4, 5 implies that if such a graph G exists, then it must
have six vertices. We notice that three of these vertices are even and three are odd.
Theorem 2.2 states that every graph contains an even numb
Key for homework 1
1. The denition of a digraph is exactly the same as a graph, except that a graph
must also be symmetric. Hence, a symmetric digraph has exactly the same denition
as a graph. A symmetric digraph, however, is drawn somewhat dierently. In
MATH 150 (Kincaid/MW 2-3:30)
First-year Seminar: Graphs and Complex Networks
Answers to selected exam 1 questions
1. The graph is irreexive since for every x V (x, x) R. The graph is
not symmetric since (q, e) R but (e, q ) R. Moreover, since the graph
is