Graph Matching

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What is graph matching?

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Graph matching is the process of finding a set of edges in a graph such that no two edges share a common vertex. It is used to pair elements from two sets based on certain criteria.

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What is a vertex in a graph?

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A vertex (or node) is a fundamental part of a graph, representing a point where edges meet. In a graph, vertices are used to represent objects or entities.

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What is an edge in a graph?

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An edge is a connection between two vertices in a graph. It can represent a relationship or a pathway between the objects represented by the vertices.

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What is a bipartite graph?

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A bipartite graph is a type of graph where the vertices can be divided into two distinct sets such that no two graph vertices within the same set are adjacent.

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What is the degree of a vertex?

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The degree of a vertex is the number of edges connected to it. It indicates how many connections or relationships the vertex has.

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What is a perfect matching in a graph?

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A perfect matching is a matching that covers every vertex of the graph exactly once, meaning every vertex is paired with exactly one other vertex.

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What is a matching in graph theory?

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A matching is a set of edges without common vertices. It pairs vertices together in a way that no two edges share a vertex.

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What is an isomorphic graph?

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Two graphs are isomorphic if there is a one-to-one correspondence between their vertices and edges, preserving the connectivity.

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What is a weighted graph?

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A weighted graph is a graph in which each edge has a numerical value (weight) associated with it, often representing costs, distances, or capacities.

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What is a path in a graph?

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A path is a sequence of edges that connects a sequence of vertices. It can be simple (no repeated vertices) or can include cycles.