# Eulerian and hamiltonian graph

I am currently work on a problem about these two graphs I mentioned in the title:

• The maximum node degree is: $8$ because there are 8 nodes
• The graph has subgraphs: $8$ because of the 8 nodes(every node could be a subgraph)
• Is the graph an Eulerian graph: $YES$
• Is the graph an hamiltonian graph: $NO$
• Is this graph an acyclic graph: $NO$ because there are cycles in this graph
• Does the graph contains a spanning subtree:$YES$ because when you connect every outer border with a node you get a spanning subtree

Are my argumentations correct?

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You will have to translate some of the German adjectives to English. For example, ‘eulerscher’ should be ‘Eulerian’ and ‘hamiltonischer’ should be ‘Hamiltonian’. Also, I would like to see the definition of an ‘exciting tree’. :) –  Haskell Curry Jan 15 '13 at 10:41
I think one of the two "eulerscher" in the third and fourth bullets should be "hamiltonischer", or are you undecided? :) It might help to see how you got those numbers for the maximum node degree, the number of subgraphs, etc. –  Martin Jan 15 '13 at 10:51
@HaskellCurry yes you are right, its hard if you only have a german textbook to translate it into proper english... btw I updated my post;) –  Le Chifre Jan 15 '13 at 10:57
The maximum node degree is 4 not 8! –  Jernej Feb 28 '13 at 8:41
The degree of a node is the number of edges incident with the given node. Which vertex has the maximal number of incident edges to it and how many? –  Jernej Mar 4 '13 at 8:44