There is many-a-kind of number,

which sometimes makes me feel dumber.

Let's say that we start from zero to four,

and see if that leads us to learn some more.

Some numbers you might see as a product,

taken from a cart, just so you got it.

These numbers have special twins that keep it real,

and in so doing their nature conceal.

Relations are a part of all kinds graphs,

big ones, small ones, and also digraphs.

At the risk of a little frustration,

oh please oh please tell me,

what is my relation?

enter image description here

Hint 1

The nodes have some sort of relation to complex numbers.


Answer with two options

the product of complex conjugates $(x+yi)(x-yi) = x^2+y^2$ or $(z+zi)(z-zi) = z^2+z^2$

where $x, y$ represent values of parent nodes and $z$ represent the value from single parent node in terms of the graph.


Partial answer

The nodes $x$ and $y$ connect to $x^2+y^2$ (e.g. $0$ and $4$ to $0^2+4^2=16$, $1$ and $2$ to $1^2+2^2=5$ etc.). If $x=y$, it's only 1 edge. The relation to complex numbers may be that $x^2+y^2$ is the squared absolute value of $x+yi$, i.e. $|x+yi|^2=x^2+y^2$, or the product of complex conjugates $(x+yi)(x-yi)$. So, the relation can be complex conjugation.

  • $\begingroup$ Your last sentence is nearly right, and in the context of what you've said before you I can tell you have it. Can you reword to the exact relation? $\endgroup$ – Galen Apr 26 '20 at 17:38
  • $\begingroup$ I mean a relation in terms of the graph, though you have stated the relation mentioned in Hint 1. That confusion is my doing. $\endgroup$ – Galen Apr 26 '20 at 17:39

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