A simple path in a graph is a path that contains no repeated vertices, and (therefore) no cycles. Let G be an undirected graph and consider the languages: SPATH = { | G has a simple path of length | G has a simple path of length 2 k from a to b} a. Show that SPATH E P. b. Show that LPATH is NP-complete.

Q: Hall’s

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A: SUMMARY: - hence, we discussed all the points.

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Adjacency matrix representation

An adjacency matrix is a square matrix that represents a finite graph. The matrix denotes whether a particular pair of nodes in a graph is adjacent or not. In brief, an adjacency matrix is an array of size N x N, where N is the number of vertices in the graph. The adjacency matrix can be used to represent a directed graph, undirected graph or a weighted graph.