Classwork Quiz Worksheet Homework (day 54) Worksheet (1-7) Walks, Paths and Circuits SOL: DM.1

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. A bridge in a connected graph is an edge such that if it were removed the graph is no longer connected. What is the bridge? The red segment

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.

1. Use the fewest number of colors possible to properly color each map. Hint: Put a dot in each region. Connect where they touch. Vertex drawing is only the dots and lines……or Cover with white paper. Mark all regions. Connect what touches. Pick-up paper and that is the vertex drawing. 2.Determine how many vertices and how many edges each graph has. Find the degree of each vertex. Then add the degrees to get the sum of the degrees of the vertices of the graph. What relationship do you notice between the sum of the degrees and the number of edges?

3. Highlight the disconnected graph(s). 5. Which of the following are walks in the graph. Justify.

6. Determine whether the sequence of the vertices is a walk, a path and/or a circuit in the graph using the diagram. 7. Determine whether the graph(s) are a complete graph. Justify.