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Math 1100 Final Exam || A+ Graded Already.
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  • Course
  • Math 1100
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  • Math 1100

Graph correct answers a simple picture that represents some kind of relationships or connections. Composed of vertices that are connected by edges. Edges correct answers joins two vertices; always end at vertices vertex correct answers end of an edge; or isolated point Valence correct answ...

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  • September 17, 2024
  • 4
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers

Subjects

  • graph

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  • Math 1100
  • Math 1100

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Math 1100 Final Exam || A+ Graded Already.
Graph correct answers a simple picture that represents some kind of relationships or connections.
Composed of vertices that are connected by edges.

Edges correct answers joins two vertices; always end at vertices

vertex correct answers end of an edge; or isolated point

Valence correct answers number of ends of edges connected to the vertex

isomorphic graphs correct answers Show the same information but are drawn differently

path correct answers any connected sequence of edges (abcd)

circuit correct answers a path that starts and ends at the same vertex (abca)

connected graph correct answers every pair of vertices is connected by some path

Euler Circuit correct answers starts at a vertex, crosses each edge exactly once, and ends at
starting vertex

Euler Theorm : Does this path have an euler circuit? correct answers 1. the graph is connected
2. all vertices have even valences

Euler Path correct answers covers each edge exactly once, but may not end at starting vertex

How to tell if a graph has an euler path? correct answers If 2 or fewer vertices have odd valences
and the graph is connected
(odd vertices begin and end path)

Postman Problem correct answers add edges until every valence is even

hamiltonian circuit correct answers use every vertex exactly once (skip some edges)
returns to where it started

complete graph correct answers A graph in which every vertex is directly connected by an edge
to each of the other vertices.

Nearest Neighbor Algorithm correct answers 1. pick any starting vertex
2.move to an adjacent vertex along the best allowable edge (has not been used; does not block
you from completing the hamiltonian circuit)
3. continue until you have visited each vertex exactly once and have returned to the starting
vertex

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