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A graph where there's a path between every pair of vertices. Example: Any tree is a connected graph.

A graph formed by connecting a single central vertex to all vertices of a cycle. Example: $W_4$, a wheel graph with 4 vertices forming a triangle with a center vertex.

A graph where every pair of vertices is connected by a unique edge. Example: $K_5$, the complete graph on 5 vertices.

A graph that forms a single closed loop. Example: $C_4$, the cycle graph with 4 vertices forming a square.

An acyclic connected graph. Example: A binary tree.

A graph where all vertices have degree 3. Example: The graph formed by the edges and vertices of a cube.

A graph that can be drawn on a plane without crossing edges. Example: The graph of a cube.

A graph that has a closed trail containing all edges of the graph, where each edge is used exactly once. Example: A cycle graph is Eulerian.

A graph where vertices are arranged in a line. Example: $P_4$, a path graph with 4 vertices.