There is given a graph $G$ and its adjacency matrix $A(G)$
I ask a quite general question:
Assume that graph $G$ contains a $k$-clique. How does this affect on behaviour of $A(G)$? How to detect a clique in a clever way using $A(G)$?
By writing "clever way" i meant that not to just looking at exemplary matrix, but rather at its properties. Suppose that we have given any adjacency matrix, then deciding whether it has a clique by looking at it is impossible.
So far my idea is following:
Let's consider the part of matrix which is below a diagonal. Let's call it $B$. Then to each column of $B$ we write a sum of the elements in that given column. The same with rows.
Having that values can we determine $B$?
Using that values can we detect a clique in $B$?
Regards.