Graphs and Their Applications

What is the definition of graphs?

• A graph is a mathematical function that describes relationships.
• A graph is a collection of numbers used in statistics.
• A graph is a type of chart used for data visualization.
• A graph is a collection of vertices connected by edges.

What are finite and infinite graphs?

• Finite graphs can only have one vertex and no edges.
• Finite graphs have a limited number of vertices and edges, while infinite graphs have an unlimited number of vertices and/or edges.
• Infinite graphs are always connected and cannot have isolated vertices.
• Finite graphs can have an infinite number of edges.

What is an isolated vertex?

• A vertex that is part of a cycle.
• A vertex that connects to multiple edges.
• A vertex that has at least one edge.
• A vertex with no edges.

What is a pendant vertex?

• A pendant vertex is a vertex that has no connections to other vertices.
• A pendant vertex is a vertex connected to two other vertices.
• A pendant vertex is a vertex connected to exactly one other vertex.
• A pendant vertex is a vertex that forms a cycle with other vertices.

What is a null graph?

• A null graph is a graph with one vertex and no edges.
• A null graph is a graph with no vertices and no edges.
• A null graph is a graph with multiple vertices and no edges.
• A null graph is a graph with edges but no vertices.

What are paths and circuits?

• A path consists of edges only, while a circuit consists of vertices only.
• A path is a sequence of vertices connected by edges without repetition, while a circuit is a path that starts and ends at the same vertex without revisiting other vertices.
• A path is a closed loop, while a circuit is an open sequence of edges.
• A path is a loop that revisits vertices, while a circuit is a straight line between two points.

What is isomorphism in graphs?

• Isomorphism in graphs is a mapping between two graphs that preserves their structure.
• Isomorphism in graphs is a method to calculate graph density.
• Isomorphism in graphs refers to the number of vertices in a graph.
• Isomorphism in graphs is a type of graph coloring.

What are sub graphs?

• A subgraph is a graph that contains all the vertices of the original graph.
• A subgraph is a graph that includes only the edges of the original graph.
• A subgraph is a graph formed from a subset of the vertices and edges of another graph.
• A subgraph is a graph that cannot be formed from another graph.

What is a puzzle with multicolored cubes?

• Jigsaw Puzzle
• Chess Set
• Tetris Blocks
• Rubik's Cube

What are walks in graph theory?

• do not allow revisits

• sequences of vertices and edges where each edge connects two vertices, allowing revisits.

• A collection of disconnected vertices
• Only sequences of edges without vertices