 
Summary: Graph Theory Worksheet Math 105, Fall 2010 Page 1
Eulerizations and Trees
1. Find an Eulerization and a SemiEulerization for the following graphs:
(a)
(b)
(c)
(d)
(e)
Graph Theory Worksheet Math 105, Fall 2010 Page 2
2. (a) Draw a connected graph with 4 vertices and no circuits. How many edges does it
have?
(b) Draw a connected graph with 5 vertices and no circuits. How many edges does it
have?
(c) Draw a connected graph with 6 vertices and 5 edges. Does it have any circuits?
(d) Draw a connected graph with 7 vertices and 6 edges. Does it have any circuits?
Graph Theory Worksheet Math 105, Fall 2010 Page 3
A tree is a connected graph (network) with no circuits. Any tree with N vertices has
N  1 edges, and any connected graph (network) with N vertices and N  1 edges is
a tree!
A spanning tree of a network is a subgraph (graph within a graph) that connects all
