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Eulerian Graph -- from Wolfram MathWorld

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An Eulerian graph is a graph containing an Eulerian cycle. The numbers of Eulerian graphs with , 2, ... nodes are 1, 1, 2, 3, 7, 15, 52, 236, ... (OEIS A133736), the first few of which are illustrated above. The corresponding numbers of connected Eulerian graphs are 1, 0, 1, 1, 4, 8, 37, 184, 1782, ... (OEIS A003049; Robinson 1969; Liskovec 1972; Harary and Palmer 1973, p. 117), the first few of which are illustrated above. Some care is needed in interpreting the term, however, since some authors define an Euler graph as a different object, namely a graph for which all vertices are of even degree (motivated by the following theorem). Euler showed (without proof) that a connected simple graph is Eulerian iff it has no graph vertices of odd degree (i.e., all vertices are of even degree). While the number of connected Euler graphs on nodes is equal to the number of connected Eulerian graphs on nodes, the counts are different for disconnected graphs since there exist disconnected graphs

Eulerian Graph -- from Wolfram MathWorld Eulerian Graph Download Wolfram Notebook An Eulerian graph is a graph containing an Eulerian cycle . The numbers of Eulerian graphs with , 2, ... nodes are 1, 1, 2, 3, 7, 15, 52, 236, ... (OEIS A133736 ), the first few of which are illustrated above. The corresponding numbers of connected Eulerian graphs are 1, 0, 1, 1, 4, 8, 37, 184, 1782, ... (OEIS A003049 ; Robinson 1969; Liskovec 1972; Harary and Palmer 1973a, p. 117), the first few of which are illustrated above. Some care is needed in interpreting the term, however, since some authors define an Eu

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