Introduction. The number of connected linear graphs having V vertices labelled 1, … , V and λ (unlabelled) lines is found below. Similar formulas are found for graphs in which slings, lines “in parallel,” or both are allowed and for directed graphs with or without slings or parallel lines. Some of these graphs are also counted when the lines are labelled and the vertices are unlabelled.
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E. N. Gilbert (1956) studied this question.
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