Problem Set 6 Solutions
نویسنده
چکیده
Problem 1. [20 points] The adjacency matrix A of a graph G with n vertices as defined in lecture is an n×n matrix in which Ai,j is 1 if there is an edge from i to j and 0 if there is not. In lecture we saw how the smallest k where Ai,j 6= 0 describes the length of the shortest path from i to j. Given a combinatorial interpretation of the following statements about the adjacency matrix in terms of connectivity properties of G. For example, the smallest k such that Ai,j is non-zero means that the distance from i to j is at most k.
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