A subgraph is a graph formed from a subset of the vertices and edges of another graph.

A subgraph is a graph that contains all the vertices and edges of the original graph.

A subgraph is a graph that cannot exist independently of the original graph.

A subgraph is a graph that includes only the edges of the original graph.

Calculating the area of a graph

Sorting vertices in alphabetical order

Adding/removing vertices and edges, traversing, finding shortest paths, checking connectivity, graph transformations.

Drawing graphs on paper

A walk is a sequence of vertices connected by edges; a path is a walk with distinct vertices; a circuit is a closed walk starting and ending at the same vertex.

A walk is a closed loop with no repeated edges; a path is a walk with some repeated vertices; a circuit is a sequence of edges without any vertices.

A walk is a collection of edges; a path is a walk that includes all vertices; a circuit is a walk that visits every edge exactly once.

A walk is a single edge; a path is a walk that can revisit vertices; a circuit is a walk that does not return to the starting vertex.

Connected graphs have paths between all pairs of vertices; disconnected graphs do not.

Connected graphs have more edges than disconnected graphs.

Disconnected graphs can have paths between some pairs of vertices.

Connected graphs can be split into multiple components without losing edges.

Graph components are the connected subgraphs of a graph.

Graph components are the overall structure of a graph.

Graph components are the edges connecting vertices.

Graph components are the vertices of a graph.

Graph homomorphism is a type of isomorphism.

Graph homomorphism requires a one-to-one mapping.

Isomorphism allows for structure changes between graphs.

Graph homomorphism preserves structure; isomorphism is a bijective homomorphism.

Eulerian graphs have a trail visiting every edge once; Hamiltonian graphs have a cycle visiting every vertex once.

Both Eulerian and Hamiltonian graphs have trails visiting every edge and vertex respectively.

Eulerian graphs have a cycle visiting every edge once; Hamiltonian graphs have a trail visiting every vertex once.

Eulerian graphs have a cycle visiting every vertex once; Hamiltonian graphs have a trail visiting every edge once.

A planar graph is a graph that can only be drawn in three dimensions.

A planar graph is a type of graph that has no vertices.

A planar graph is a graph that can be drawn on a plane without edge crossings.

A planar graph is a graph that can have multiple edges crossing each other.

Graph theory is primarily focused on statistical analysis of data.

Graph theory has no applications in real-world scenarios.

Real-life applications of graph theory include transportation networks, social network analysis, computer network management, and logistics optimization.

Graph theory is used exclusively in video game design.