Given an undirected non-weighted graph edges.
'1#2', '2#3', '1#11', '3#11', '4#11', '4#5', '5#6', '5#7', '6#7', '4#12', '8#12', '9#12', '8#10', '9#10', '8#9'
where for example node 1 and node 2 is having a direct edge
now the question is, which algorithm can be used to find the maximum no. of nodes that can be visited (starting from any node), visiting a node atmost once and no traversing back by any edge
Best Answer
Your problem is the Longest path problem and is known to be NP-hard.
Hence there is no known polynomial time algorithm to answer your problem, and unless P=NP there are no such algorithm.
So to answer your question you may as well enumerate all the possible path visiting at most once each vertex and find the longest.