Walks, Paths and Circuits. A graph is a connected graph if it is possible to travel from one vertex to any other vertex by moving along successive edges.

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Presentation transcript:

Walks, Paths and Circuits

A graph is a connected graph if it is possible to travel from one vertex to any other vertex by moving along successive edges. A graph is a disconnected graph if it is not possible to travel from one vertex to any other vertex by moving along successive edges. Examples:

A Bridge in a connected graph is an edge such that if it were removed the graph is no longer connected.

Vocabulary A walk is a series of adjacent vertices that can go backwards as long as there is a line segment. A path is a walk which does not repeat vertices. A Circuit is a path whose endpoints are the same vertex. Note: you start and finish with the same vertex without repeating any edges.