MathJax


Saturday, March 7, 2026

2026-316

Consider the following graph and the subsequent statements:


1. The graph is connected because the links (0, 1), (0, 2) and (0, 3) intersect with the links (4, 5), (4, 6) and (5, 6).

2. If we consider the components of this graph as projections of a bipartite graph, the parent bipartite graph could be:

3. The adjacency matrix of this graph can be rearranged and separated into two non-zero submatrices of size 4x4 and 3x3.

The correct statements are:

a) Just 3

b) 1 and 2

c) 1 and 3

d) 2 and 3

e) None of the above.


Original idea by: Rafael Brusiquesi Martins

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2026-318

Suppose a graph \(G\) has the following second power of the adjacency matrix: $$ A^2 = \left( \begin{array}{cccc}1 & 0 & 1 & 1\...