   # Pets The diagram below shows the arrangement of a Habitrail cage for a pet hamster. (Plastic tubes connect different cages.) Is it possible for a hamster to travel through every tube without going through the same tube twice? If so, find a route for the hamster to follow. Can the hamster return to its starting point without repeating any tube passages? ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.1, Problem 27ES
Textbook Problem
880 views

## Pets The diagram below shows the arrangement of a Habitrail cage for a pet hamster. (Plastic tubes connect different cages.) Is it possible for a hamster to travel through every tube without going through the same tube twice? If so, find a route for the hamster to follow. Can the hamster return to its starting point without repeating any tube passages? To determine

To determine if it is possible for a hamster to travel through every tube without going through the same tube twice. And if it can, to find the route for the hamster to follow. To check if the hamster can return to its starting point without repeating any tube passages.

### Explanation of Solution

Given information:

Given, the diagram below shows the arrangement of a Habitrail cage for a pet hamster. (Plastic tubes connect different cages.)

Calculation:

To check the possibility of the travel, the arrangement is to be graphed.

Every cage is considered as a vertex and every pipe is considered an edge.

Also, there are two intersections of pipe where there is no cage but are to be considered vertices as that part of pipe can be considered as another edge.

Using the above image, the graph can be made as:

It is possible for a hamster to travel through every tube without going through the same tube twice if the graph satisfies the condition of either Euler circuit or Euler path.

An Eulerian graph (that starts and ends at the same vertex) is said to be Euler circuit if it uses every edge, but only once. (i.e. no edge is used more than once).

Euler path is defined as the path in a connected graph that has exactly two vertices of odd degree with all the remaining vertices of even degree and the path starts at one of the vertices with odd degree and ends at the other vertex with odd degree...

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