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Answer: In Exercises 29 through 34 choose from one of the following answers and provide
Chapter 5, Problem 32(choose chapter or problem)
In Exercises 29 through 34 choose from one of the following answers and provide a short explanation for your answer. (A) the graph has an Euler circuit. (B) the graph has an Euler path. (C) the graph has neither an Euler circuit nor an Euler path. (D) the graph may or may not have an Euler circuit. (E) the graph may or may not have an Euler path. You do not have to show an actual path or circuit.(a) Fig. 44(a) (b) Fig. 44(b) (c) A disconnected graph with eight vertices: six verticesof degree 2 and two vertices of degree 3
Questions & Answers
QUESTION:
In Exercises 29 through 34 choose from one of the following answers and provide a short explanation for your answer. (A) the graph has an Euler circuit. (B) the graph has an Euler path. (C) the graph has neither an Euler circuit nor an Euler path. (D) the graph may or may not have an Euler circuit. (E) the graph may or may not have an Euler path. You do not have to show an actual path or circuit.(a) Fig. 44(a) (b) Fig. 44(b) (c) A disconnected graph with eight vertices: six verticesof degree 2 and two vertices of degree 3
ANSWER:Step 1 of 5
(a)
Basic Definitions to be known
• Degree: number of edges meeting at the vertex, then that number represent the degree of vertex.
• Path: a sequence of edges each adjacent to the next, with no edge included more than once, and starting and ending at different vertices
• Euler path: a path that travels along each edge of a graph once and only once
• Euler circuit: a circuit that travels along each edge of a graph once and only once and starts and end at the same vertex.
• Connected graph: a graph such that there is a path going from any vertex to any other vertex
• Disconnected graph: a graph that is not connected; it has two or more connected components
• Components: the connected “pieces” that make up a graph