How to translate the problem into a Communication Matrix?

Question

Description of the problem:

Alice and Bob are both given as input the same graph and vertex $x$ and $y$ respectively. In the graph there are no self-loops and the given vertex can be the same.

Prove that communication complexity between Alice and Bob for deciding whether $x$ and $y$ are neighbours is at least $log \chi (G)$.

Current Idea:

The idea I had was the following: represent the protocol for communication between Alice and Bob as a Communication Matrix and partition it with monochromatic rectangles. From there I want to use the theorem/fact: $D^{CC}(f) \geq log (part(f))$ where $part(f)$ is the least number of monochromatic rectangles in any partition.

Problem:

I am not sure how this problem can be translated into a Communication Matrix. Would the inputs be vertices and then 1 would indicate presence of an edge and 0 otherwise?

Answer 1

As @jschnei has mentioned in the comment, the answer is:

The communication matrix has rows indexed by Alice's inputs, columns indexed by Bob's input, and value f(x, y) at the cell in the row corresponding to Alice's input x and Bob's input y. In this case, when x and y are any vertices of a graph G, this should give rise to a very familiar matrix.