Math 100 Final exam Test Questions And
Answers Verified 100% Correct
spanning tree - ANSWER -We can get one by picking just enough of a graph's
original edges so the result is connected.
spanning tree - ANSWER -A connected, spanning subgraph w/ no cycles.
Euler Characteristic Equation - ANSWER -In the plane or on the surface of a
sphere, it's
𝑉 + 𝐹 − 𝐸 = 2. (Or you can say, 𝑉 − 𝐸 + 𝐹 = 2)
Euler Characteristic Equation - ANSWER -This applies to connected graphs that
you can draw without edges crossing.
Platonic (a.k.a. Regular) Solid - ANSWER -There are only five types of
________.
Minimum-Cost Spanning Tree - ANSWER -A spanning tree where the total cost
of the
edges is as low as possible.
Minimum-Cost Spanning Tree - ANSWER -We can use Kruskal's algorithm to
find one.
Subdivision - ANSWER -A ______ of a graph is what we get when we replace at
least one edge of that graph with a longer path.
Bipartite Graph - ANSWER -Even with just two colors, you can color the vertexes
without giving adjacent vertexes the same color.
, Bipartite Graph - ANSWER -We can organize the vertexes into two "families" so
that no two vertexes from the same "family" share an edge.
𝐾5 - ANSWER -A complete graph on five vertexes
𝐾5 - ANSWER -A simple graph with five vertexes and an edge for every pair of
vertexes.
𝐾3,3 - ANSWER -A complete bipartite graph on three and three vertexes.
𝐾3,3 - ANSWER -A simple graph that is not planar and has 𝑉 = 6, 𝐸 = 9.
Fractal - ANSWER -You can keep zooming in on any part of it and there is no
limit to the detail you would keep discovering.
Fractal - ANSWER -Its dimension might not be an integer.
Coastline Paradox - ANSWER -"How long is the coast?" doesn't have a good
ANSWER
Continuous Function - ANSWER -As the inputs get closer the outputs tend to get
closer; and there is no restriction on how close the outputs can tend to get if your
inputs get
Continuous Function - ANSWER -If the input 𝑎 gives a negative output and the
input 𝑏 gives a positive output, somewhere between 𝑎 and 𝑏 must be an input that
gives zero as the output.
Arrow's Impossibility Theorem - ANSWER -Every ordinal voting system must be
unfair in
at least one scenario.
Kuratowski's Theorem - ANSWER -The non-planar graphs are exactly those
which
Answers Verified 100% Correct
spanning tree - ANSWER -We can get one by picking just enough of a graph's
original edges so the result is connected.
spanning tree - ANSWER -A connected, spanning subgraph w/ no cycles.
Euler Characteristic Equation - ANSWER -In the plane or on the surface of a
sphere, it's
𝑉 + 𝐹 − 𝐸 = 2. (Or you can say, 𝑉 − 𝐸 + 𝐹 = 2)
Euler Characteristic Equation - ANSWER -This applies to connected graphs that
you can draw without edges crossing.
Platonic (a.k.a. Regular) Solid - ANSWER -There are only five types of
________.
Minimum-Cost Spanning Tree - ANSWER -A spanning tree where the total cost
of the
edges is as low as possible.
Minimum-Cost Spanning Tree - ANSWER -We can use Kruskal's algorithm to
find one.
Subdivision - ANSWER -A ______ of a graph is what we get when we replace at
least one edge of that graph with a longer path.
Bipartite Graph - ANSWER -Even with just two colors, you can color the vertexes
without giving adjacent vertexes the same color.
, Bipartite Graph - ANSWER -We can organize the vertexes into two "families" so
that no two vertexes from the same "family" share an edge.
𝐾5 - ANSWER -A complete graph on five vertexes
𝐾5 - ANSWER -A simple graph with five vertexes and an edge for every pair of
vertexes.
𝐾3,3 - ANSWER -A complete bipartite graph on three and three vertexes.
𝐾3,3 - ANSWER -A simple graph that is not planar and has 𝑉 = 6, 𝐸 = 9.
Fractal - ANSWER -You can keep zooming in on any part of it and there is no
limit to the detail you would keep discovering.
Fractal - ANSWER -Its dimension might not be an integer.
Coastline Paradox - ANSWER -"How long is the coast?" doesn't have a good
ANSWER
Continuous Function - ANSWER -As the inputs get closer the outputs tend to get
closer; and there is no restriction on how close the outputs can tend to get if your
inputs get
Continuous Function - ANSWER -If the input 𝑎 gives a negative output and the
input 𝑏 gives a positive output, somewhere between 𝑎 and 𝑏 must be an input that
gives zero as the output.
Arrow's Impossibility Theorem - ANSWER -Every ordinal voting system must be
unfair in
at least one scenario.
Kuratowski's Theorem - ANSWER -The non-planar graphs are exactly those
which
