Question

Give an example of a connected undirected graph that contains at least twelve vertices that contains at least two circuits. Draw that graph labeling the vertices with letters of the alphabet. Determine one spanning tree of that graph and draw it. Determine whether the graph has an Euler circuit. If so, specify the circuit by enumerating the vertices involved. Determine whether the graph has an Hamiltonian circuit. If so, specify the circuit by enumerating the vertices involved.

Answer #1

Draw an undirected graph with 6 vertices that has an Eulerian
Cycle and a Hamiltonian Cycle. The degree of each vertex
must be greater than 2. List the degrees of the
vertices, draw the Hamiltonian Cycle on the graph and give the
vertex list of the Eulerian Cycle.
Draw a Bipartite Graph with 10 vertices that has an Eulerian
Path and a Hamiltonian Cycle. The degree of each vertex
must be greater than 2. List the degrees of the
vertices, draw the Hamiltonian Cycle...

10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the edge set?
Construct a bipartite graph with vertices Q,R,S,T,U,V,W such
that the degree of S is 4.
What is the edge set?
12.-Construct a simple graph with vertices F,G,H,I,J that has an
Euler trail, the degree of F is 1 and the degree of G is 3.
What is the edge set?
13.-Construct a simple graph with vertices L,M,N,O,P,Q that has
an Euler circuit...

Let G be a connected simple graph with n vertices and m edges.
Prove that G contains at least m−n+ 1 different subgraphs
which are polygons (=circuits). Note: Different polygons
can have edges in common. For instance, a square with a diagonal
edge has three different polygons (the square and two different
triangles) even though every pair of polygons have at least one
edge in common.

The Business Case for Agility
“The battle is not always to the strongest, nor the
race to the swiftest, but that’s the way to bet
’em!” —C. Morgan Cofer
In This Chapter
This chapter discusses the business case for Agility,
presenting six benefits for teams and the enterprise. It also
describes a financial model that shows why incremental development
works.
Takeaways
Agility is not just about the team. There are
product-management, project-management, and technical issues beyond
the team’s control. Lean-Agile provides...

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