CS6515 Exam 2 2025 (Actual Exam) Questions
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Terms in this set (71)
, Tree's are undirected, connected and acyclic that
connect all nodes.
1. Tree on n vertices has (n-1) edges -> would have a
cycle otherwise (more than n-1 edges means cycle)
Basic Properties of Trees
2. In tree exactly one path between every pair of
vertices (otherwise it's not connected)
- More than 1 path implies cycle
- less than 1 path implies not connected
3. Any connected G(V, E) with |E| = |V| - 1 is a tree
1. Sort E by increasing weigt
2. Go through edges in order and add an edge to our
Kruskal's Algorithm current tree if it doesn't create a cycle
Running Time: O(m log n), m = |E|, n = |V|
Is there ever a reason to No
use cycles in a flow
graph?
Flow Network Constraints: For all edges, the flow must be larger than zero, but
Capacity Constraint less than the capacity of that edge
Maximize the flow out of the source (or into the sink)
Goal of Flow Problem of maximum size while satisfying the capacity and
conservation of flow constraints.
For all vertices (other than the starting (source) and
Flow Network Constraints:
ending (sink) vertices), the flow into v must equal the
Conservation of Flow
flow out of v.
with verified Answers (Latest Update 2025)
UPDATE!!
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Practice questions for this set
Learn 1 /7 Study with Learn
Terms in this set (71)
, Tree's are undirected, connected and acyclic that
connect all nodes.
1. Tree on n vertices has (n-1) edges -> would have a
cycle otherwise (more than n-1 edges means cycle)
Basic Properties of Trees
2. In tree exactly one path between every pair of
vertices (otherwise it's not connected)
- More than 1 path implies cycle
- less than 1 path implies not connected
3. Any connected G(V, E) with |E| = |V| - 1 is a tree
1. Sort E by increasing weigt
2. Go through edges in order and add an edge to our
Kruskal's Algorithm current tree if it doesn't create a cycle
Running Time: O(m log n), m = |E|, n = |V|
Is there ever a reason to No
use cycles in a flow
graph?
Flow Network Constraints: For all edges, the flow must be larger than zero, but
Capacity Constraint less than the capacity of that edge
Maximize the flow out of the source (or into the sink)
Goal of Flow Problem of maximum size while satisfying the capacity and
conservation of flow constraints.
For all vertices (other than the starting (source) and
Flow Network Constraints:
ending (sink) vertices), the flow into v must equal the
Conservation of Flow
flow out of v.
