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I construct a graph but I don't know whether it is well known. A closely related graph is the Hamiltonian cycle, but in my graph there are an extra node and an edge. My graph consists of a Hamiltonian cycle and a edge from a node on Hamiltonian cycle. Is the graph well known?

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 It would probably be helpful to have a picture of the graph to help decide if it is known. As Hamiltonian cycles appear in many graphs, that does not help narrow it down. – ARupinski Jan 27 2011 at 20:33
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 Or if not a picture, at least a description of how you built your graph so that others can reconstruct it in order to answer the question. – ARupinski Jan 27 2011 at 20:34
If nothing else, you could provide a graphviz description of the graph for us to build and visualize :) – copumpkin Jan 27 2011 at 20:47
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 "Consists" implies that your graph is nothing but a cycle plus an edge from a node in the cycle to a node not in the cycle. Maybe you want to say your graph "contains" a graph with a Hamiltonian cycle together with an edge from a node in that cycle to a node not in it. Whatever. I'm voting to close, pending clarification of what the question really is. – Gerry Myerson Jan 27 2011 at 22:01
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 I'm also voting to close. The question is very unclear. "The Hamiltnian cycle" is not "a graph": it is a sub-graph of a given graph. Are we talking about a single graph? Or is there a whole family of graphs? – André Henriques Jan 28 2011 at 0:09
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closed as not a real question by Gerry Myerson, André Henriques, Douglas Zare, Aaron Meyerowitz, Pete L. Clark Jan 28 2011 at 6:28

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