Noneulerian Graph

Author

Eric W. Weisstein
February 8, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/NoneulerianGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/NoneulerianGraph.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Counts

Count[#,_?(!EulerianQ[#]&)]&/@Graphs/@Range[9]//Timing

Count[#,_?(!EulerianQ[#]&)]&/@ConnectedGraphs/@Range[9]//Timing

Count[#,_?(!EulerianQ[#]&)]&/@ConnectedGraphs/@Range[9]//Timing

Euler transform of A007126(n+1)

Date: Thu, 12 Mar 2009 16:16:39 +0100
From: Vladeta Jovovic <vladeta@eunet.yu>
Reply-To: Sequence Fanatics Discussion list <seqfan@list.seqfan.eu>

http://www.research.att.com/~njas/sequences/A007126

Number of connected rooted strength 1 Eulerian graphs with n nodes.

Tests

GraphData[{"Bridged","Eulerian"}]

Select[GraphData[All],!GraphData[#,"Noneulerian"]&&GraphData[#,"Bridged"]&]

Select[GraphData[All],GraphData[#,"Noneulerian"]&&OddQ[Or@@GraphData[#,"Degrees"]]&]

Table

Sort[{GraphData[#,"Name"],GraphData[#,"VertexCount"]}&/@GraphData["Noneulerian"],Last[#1]<=Last[#2]&]//TableForm