Graph types
a graph that is fully connected, no separate parts
connected graph
a dot on the graph
vertex
starts and ends at same vertex, no edge repeated
cycle
a graph that has a closed cycle that uses every edge and has even degree vertices
Eularian Graph
a graph that has numbers on its edges
Weighted Graph
a graph that has no crossed over edges
planar graph
a line on the graph that connects vertices
edge
no edges or vertices repeated
path
A graph that has an open path that visits every vertex once
Semi Hamiltonian Graph
a subgraph that uses all vertices as a tree
Spanning Tree
part of an original graph
subgraph
an area of a graph that can be inside or outside
face
No edge repeated but can repeat vertex
Trail
a graph that has an open trail that uses every edge and has exactly 2 odd degree vertices
Semi Eularian Graph
a spanning tree that has the smallest possible length/weight/value of the edges.
minimum spanning tree
a graph where all vertices connect to all other vertices
complete graph
an edge that goes from a vertex back to itself
loop
can repeat vertices or edges
walk
a graph that has a closed cycle that goes through every vertex once
Hamiltonian Graph
The process where you select a vertex and then select every smallest edge one by one to connect the vertices into a minimum spanning tree
Prims Algorithm
a graph with two distinct groups
bipartite graph
the number of edges coming off a vertex
degree
another name for a closed path
cycle
Can a square complete graph be described as any of these:
a Eularian, Semi Eularian, Hamiltonian or Semi Hamiltonian?
Hamiltonian and Semi hamiltonian (Not eularian or semi Eularian)
A spanning tree will always have this many edges (something to do with its vertices)
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