anonymous
  • anonymous
What is hamaltonian graph, please explain
Computer Science
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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mathmate
  • mathmate
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.
mathmate
  • mathmate
A path traverses from one node to another, without repetition. For example: |dw:1441480351863:dw|
mathmate
  • mathmate
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.

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mathmate
  • mathmate
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
mathmate
  • mathmate
*ABCDA
mathmate
  • mathmate
For example, ABCD is a Hamiltonian path.
anonymous
  • anonymous
Thanks a lot very helpful
mathmate
  • mathmate
You're welcome! :)

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