edit: Never mind - I hadn't read far enough in. He means 'Eulerian graph', I think. As in a graph with an Eularian trail. You know it might be nice for people to get the terminology right if you are writing about this stuff...

What do you mean by 'Euler graphs'? As in, the problems described by him such as the bridge problem?

I would call anything with vertices and edges an 'Euler graph' as opposed to a 'Cartesian graph' (a chart).