Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY
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Transcript of Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY
Can you draw this picture without lifting up your pen/pencil?
How about this one?
Section 5.3 GRAPH CONCEPTS AND
TERMINOLOGY
• 1) Degree of a vertex - the number of edges at the vertexa) a loop counts twiceb) odd vertex - a vertex of odd degreec) even vertex - a vertex of even degree
List all of the odd vertices: __________________
List even vertices: _____________________
2) Adjacent vertices - two vertices are adjacent if there is an edge joining them
3) Adjacent edges - two edges are adjacent if they share a common vertex
List a pair of adjacent vertices: __________
List a pair of adjacent edges: ___________
4) Path - a sequence of vertices such that each vertex in the sequence is adjacent to the next one and no edge appears in the path more than once.
*** The number of edges in a path is called the length of the path. Each edge has a length of 1; a loop has length of 1
List a path of length 5 from A to G:
___________________
List a path of length 7 from A to G:
___________________
5) Circuit - a path which starts and ends at the same vertex (multiple edges and loops are circuits).
List 2 circuits and give their length
_______________
_______________
6) Connected graph - a graph for which any two of its vertices can be joined by a path
7) Disconnected graph - a graph made up of connected pieces
8) Euler path - a path which travels through every edge of a graph
A
B
CD
E
Example: An Euler path: D, E, A, B, E, C, B, D, C
9) Euler circuit - a circuit which travels through every edge of a graph
Example: An Euler circuit:
D, E, A, B, E, C, B, D, C, F, D
A
B
CD
E
F
10) Bridge - an edge, which if removed, disconnects the graph
Is there a bridge?
If yes, which one?
_______________
• Draw a graph with 3 vertices, each of degree 2
• Draw a connected graph with 3 vertices, each of degree 4