🚧 Fin chapter 1

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tomit4 2026-05-24 16:37:25 -07:00
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@ -117,3 +117,65 @@ $(x, y) \in F$ and $(x, z) \in F$; $y = z$
**Solution**
a unique element of $B$ that is related to $x$ by $F$.
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**Test Yourself**
Page 57
1. A graph consists of two finite sets: _______ and _______, where each edge is
associated with a set consisting of _______.
**Solution**
a finite; nonempty set of vertices; a finite set of edges.
2. A loop in a graph is _______.
**Solution**
An edge that has a single endpoint.
3. Two distinct edges in a graph are parallel if, and only if, _______.
**Solution**
They share the same set of endpoints.
4. Two vertices are called adjacent if, and only if, _______.
**Solution**
They are connected by an edge.
5. An edge is incident on _______.
**Solution**
Each of its endpoints.
6. Two edges incident on the same endpoint are _______.
**Solution**
adjacent
7. Two edges incident on the same endpoint are _______.
**Solution**
isolated
8. In a directed graph, each edge is associated with _______.
**Solution**
an ordered pair of vertices called its endpoints
9. The degree of a vertex in a graph is _______.
**Solution**
the number of edges that are incident on the vertex, with an edge that is a loop
counted twice.