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What are the different ways by which we can represent graph? Represent the graph drawn below using those ways.
The different ways by which we can representgraph are:
Adjacency list representation: This representation of graph comprises of an array Adj of |V| lists, one for each vertex in V. For each uεV, the adjacency list Adj[u] comprises of all the vertices v such that there is an edge (u,v)ε E that is Adj[u] comprises of all the vertices adjacent to u in G. The vertices in each adjacency list are stored out in an arbitrary order. The adjacency list representation of given graph is depicted in the figure drawn below:
Adjacency Matrix representation: This representation consists of the |V|*|V| matrix
A= (aij) such that
The adjacency matrix representation of given graph is as follows:
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A spanning tree of any graph is only a subgraph that keeps all the vertices and is a tree (having no cycle). A graph might have many spanning trees. Figure: A Graph
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