Basics of Graph Theory

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What is a graph in graph theory?
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A graph is a collection of vertices (or nodes) and edges that connect pairs of vertices.
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What are vertices in a graph?
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Vertices, also called nodes, are points in a graph where edges meet.
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What are edges in a graph?
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Edges are the connections between pairs of vertices in a graph.
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What is a directed graph?
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A directed graph is a graph in which the edges have a direction, indicated by an arrow.
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What is an undirected graph?
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An undirected graph is a graph in which the edges have no direction.
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What is a weighted graph?
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A weighted graph is a graph in which each edge is assigned a weight or cost.
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What is a simple graph?
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A simple graph is a graph without loops and multiple edges between any two vertices.
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What is a complete graph?
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A complete graph is a graph in which every pair of vertices is connected by an edge.
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What is a path in graph theory?
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A path is a sequence of edges that connect a sequence of distinct vertices.
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What is a cycle?
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A cycle is a path that starts and ends at the same vertex, with all other vertices distinct.
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What is a connected graph?
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A connected graph is a graph in which there is a path between every pair of vertices.
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Define a subgraph.
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A subgraph is a graph formed from a subset of the vertices and edges of another graph.
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What is a degree of a vertex?
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The degree of a vertex is the number of edges incident to it.
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What is a bipartite graph?
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A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that no two vertices within the same set are adjacent.
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What is a tree in graph theory?
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A tree is a connected graph with no cycles.
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