**Determine if the given graph has a Hamilton circuit and/or a Hamilton path.****Graph Explanation:**The graph consists of 7 vertices labeled as a, b, c, d, e, f, and g. The edges between them are as follows:- Vertex a is connected to vertices b, c, d, e, f, and g.- Vertex b is connected to vertices c, d, e, and f.- Vertex c is connected to vertices f and g.- Vertex d is connected to vertices e, f, and g.- Vertex e is connected to vertex f.- Vertex f is connected to vertex g.**Options:**- ☐ The graph has neither a Hamilton circuit, nor a Hamilton path.- ☐ The graph does not have a Hamilton circuit, but has a Hamilton path.- ☐ The graph has both a Hamilton circuit and a Hamilton path.- ☐ The graph has a Hamilton circuit, but not a Hamilton path.

Hamiltonian Path: If there exists a walk in the connected graph that visits every vertex of the graph exactly once without repeating the edges,then such a walk is called Hamiltonian path. In a Hamiltonian path,edges may or may not be covered,but it should not repeat. Hamiltonian Circuit: A Hamiltonian Circuit is also known as Hamiltonian cycle. A Hamiltonian path which starts and ends at the same vertex is called Hamiltonian cycle (or) A closed Hamiltonian path is called a Hamiltonian cycle.The given graph as Hamiltonian path but not Hamiltonian circuit. The second option is correct The graph does not have a Hamiltonian circuit but has Hamiltonian path. The Hamiltonian path is : abcdegf

Math

Advanced Math

Determine if the given graph has a Hamilton circuit and/or a Hamilton path. a b f d The graph has neither a Hamilton circuit, nor a Hamilton path. The graph does not have a Hamilton circuit, but has a Hamilton path. O The graph has both a Hamilton circuit and a Hamilton path. O The graph has a Hamilton circuit, but not a Hamilton path.

Determine if the given graph has a Hamilton circuit and/or a Hamilton path. a b f d The graph has neither a Hamilton circuit, nor a Hamilton path. The graph does not have a Hamilton circuit, but has a Hamilton path. O The graph has both a Hamilton circuit and a Hamilton path. O The graph has a Hamilton circuit, but not a Hamilton path.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Determine if the given graph has a Hamilton circuit and/or a Hamilton path.**

**Graph Explanation:**

The graph consists of 7 vertices labeled as a, b, c, d, e, f, and g. The edges between them are as follows:

- Vertex a is connected to vertices b, c, d, e, f, and g.
- Vertex b is connected to vertices c, d, e, and f.
- Vertex c is connected to vertices f and g.
- Vertex d is connected to vertices e, f, and g.
- Vertex e is connected to vertex f.
- Vertex f is connected to vertex g.

**Options:**

- ☐ The graph has neither a Hamilton circuit, nor a Hamilton path.
- ☐ The graph does not have a Hamilton circuit, but has a Hamilton path.
- ☐ The graph has both a Hamilton circuit and a Hamilton path.
- ☐ The graph has a Hamilton circuit, but not a Hamilton path.

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