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anonymous

  • one year ago

What is hamaltonian graph, please explain

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  1. mathmate
    • one year ago
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    A connected graph is one which has all nodes connected by edges, as follows: |dw:1441480164362:dw| The above graph is connected because all nodes are linked to each other by edges, i.e. no islands.

  2. mathmate
    • one year ago
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    A path traverses from one node to another, without repetition. For example: |dw:1441480351863:dw|

  3. mathmate
    • one year ago
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    In the previous drawing, ABC is a path. If the starting node and the ending node are the same, the path is also a cycle. |dw:1441480530480:dw| Here, ADCBA is a cycle.

  4. mathmate
    • one year ago
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    When a cycle visits ALL the nodes of the graph without repetition, it is a Hamiltonian cycle. In the above example, ABCDE is a Hamiltonian cycle, and ADCBA is also a Hamiltonian cycle. On the other hand, if a PATH visits all the nodes on the graph (but does not return to the original node), then it is a hamiltonian path. Note: some synonyms used (probably in different countries) could be: cycle = tour path = trail For a list of downloadable books on Graph Theory, try: http://www.freebookcentre.net/Mathematics/Graph-Theory-Books.html

  5. mathmate
    • one year ago
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    *ABCDA

  6. mathmate
    • one year ago
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    For example, ABCD is a Hamiltonian path.

  7. anonymous
    • one year ago
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    Thanks a lot very helpful

  8. mathmate
    • one year ago
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    You're welcome! :)

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