Let G be a graph. The line graph L(G) of G is defined to be the graph whose vertices are the edges of G and where two vertices of L(G) are adjacent if the corresponding edges of G are adjacent. Prove that if G is connected, then L(G) is eulerian if vertices of G are all odd or all even.© BrainMass Inc. brainmass.com March 4, 2021, 8:07 pm ad1c9bdddf
It should be in your textbook but just in case here is a web reference - http://en.wikipedia.org/wiki/Eulerian_path - containing the definition of Eulerian graphs and statement saying that Eulerian graphs are connected, undirected, and their vertices are all of even degree.
Let n_i denote ...
Eulerian graphs are investigated. The solution is detailed and well presented.