Definitions in graph theory do differ from text to text. Usually anEulerian Circuitis a closed path in the graph that includes each edge exactly once.

Theorem: A simple graph has anEulerian Circuitif and only if each vertex is even.

On the other hand, a simple graph is said to beEulerianif there is path in the graph that includes each edge exactly once.

Theorem: A simple graph isEulerian Circuitif and only if there are at most two odd vertices.

Eulerian graphsare edge driven whereasHamiltonian Graphsare vertex driven. Does your given graph have a cycle that includes each vertex once.

Two graphs are isomorphic if and only if there adjacency matrices are similar.