Question

2. For the graph given below, a. Write out the degree of each vertex. b. Find an Eulerian Circuit. (Write out the sequence the vertices are traversed. E.g. A-B-C-A.) c. Find a Hamiltonian Path.

Answer 1

2.

a.) We know that the degree of a vertex in a graph is the number of edges with the particular vertex as an end point. So we see that there are four edges with A as an end point. Hence, the degree of A is 4. Similarly, we list the degrees of each vertex of the given graph, say G:

Vertices	Degree
A	4
B	2
C	2
D	4
E	4
F	2

b.) We see that the degree of each vertex is even. So we can have an Euler circuit.

$A-E-C-D-E-F-A-D-B-A$

c.) A Hamilton path is a path that visits each vertex exactly once. So, the following is a Hamilton Path:

$A-B-D-C-E-F$

Thank You.