what is bipertile graph?
Answers
Step-by-step explanation:
A bipartite graph is a graph whose vertices can be partitioned into two disjoint sets such that all the edges connect vertices from one set to vertices in the other set. ... A connected bipartite graph can be represented as a tree and vice versa. A bipartite graph does not contain cycles of odd length.
Step-by-step explanation:
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and such that every edge connects a vertex in to one in . Vertex sets and. are usually called the parts of the graph
Bipartite graphs have many applications. They are often used to represent binary relations between two types of objects. A binary relation between two sets A and B is a subset of A × B. We can see that this is equivalent to the definition of bipartite graphs as long as A and B are disjoint (i.e. A ∩ B = ∅).
A graph is said to be a bipartite graph, when vertices of that graph can be divided into two independent sets such that every edge in the graph is either start from the first set and ended in the second set, or starts from the second set, connected to the first set, in other words, we can say that no edge can found in the same set.
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A bipartite graph also called a bi-graph, is a set of graph vertices, i.e, points where multiple lines meet, decomposed into two disjoint sets, meaning they have no element in common, such that no two graph vertices within the same set are adjacent.
Adjacent nodes are any two nodes that are connected by an edge.
A bipartite graph is a special case of a k-partite graph with k = 2. The illustration below shows some bipartite graphs, with vertices in each graph colored based on the disjoint set they belong to
Bipartite graphs are equivalent to two-colorable graphs i.e., coloring of the vertices using two colors in such a way that vertices of the same color are never adjacent along an edge. All Acyclic graphs are bipartite. A cyclic graph is bipartite iff all its cycles are of even length. Some common examples of a bipartite graph include star graphs, grid graphs4 and gear graphs
Time complexity:
If V is the number of vertices and E is the number of edges, then the time complexity of a graph represented using an adjacency list will be:
O(V+E)O(V+E)
Applications of bipartite graphs:
- Bipartite graph can be used in the medical field in the detection of lung cancer, throat cancer etc.
- Used in search advertising and e-commerce for similarity ranking.
- Predict movie preferences of a person.
- Stable marriage and other matching problems.
