Context: I am studying Weisfeiler Lehman method(WL method) and have clear idea about 1 and 2 dimensional WL method. I was wondering about the individualization process described below-

Defined Individualization:

$G$ is a $r$ regular graph . $n$ th vertex of $G$ is $v_n$. All vertices which are not adjacent to $ v_n $ create a sub-graph $C_1$. All vertices adjacent to $ v_n $ create a sub-graph $, C_2 $. A vertex of $C_2$ is $ v_{n-1}$.

Using same method , based on adjacency of $ v_{n-1}$, $C_2$ can be divided.

All vertices which are not adjacent to $ v_{n-1}$ create a sub-graph $C_3$.

All vertices adjacent to $ v_{n-1}$create a sub-graph $, C_4 $. In general , $ C_{2y} $ is a graph and can be divided/ partitioned in to 2 sub graphs $ C_{2y+1}, C_{2y+2} $ .

Question:
(1) What kind of individualization is above described individualization if it exists in current literature ?

(2)Is there a relation between the above individualization and k-dimensional weisfeiler lehman method?

Motivation : Graph Isomorphism.

Context: I am studying Weisfeiler Lehman method(WL method) and have clear idea about 1 and 2 dimensional WL method. I was wondering about the individualization process described below-

Individualization:

$G$ is a $r$ regular graph . $n$ th vertex of $G$ is $v_n$. All vertices which are not adjacent to $ v_n $ create a sub-graph $C_1$. All vertices adjacent to $ v_n $ create a sub-graph $, C_2 $. A vertex of $C_2$ is $ v_{n-1}$.

Using same method , based on adjacency of $ v_{n-1}$, $C_2$ can be divided.

All vertices which are not adjacent to $ v_{n-1}$ create a sub-graph $C_3$.

All vertices adjacent to $ v_{n-1}$create a sub-graph $, C_4 $. In general , $ C_{2y} $ is a graph and can be divided/ partitioned in to 2 sub graphs $ C_{2y+1}, C_{2y+2} $ .

This method individualizes a set of $k$ vertices where $k< log_2(n)$.

Question:
Does above individualization exist in current literature ?

Initially, I thought , it is a variant of $k$ dim Wl method.

Motivation : Graph Isomorphism.

PS: Feel free to edit the post. let me know if it is still unclear.

Context: I am studying Weisfeiler Lehman method(WL method) and have clear idea about 1 and 2 dimensional WL method. I was wondering about the individualization process described below-

Defined Individualization:

$G$ is a $r$ regular graph . $n$ th vertex of $G$ is $v_n$. All vertices which are not adjacent to $ v_n $ create a sub-graph $C_1$. All vertices adjacent to $ v_n $ create a sub-graph $, C_2 $. A vertex of $C_2$ is $ v_{n-1}$.

Using same method , based on adjacency of $ v_{n-1}$, $C_2$ can be divided.

All vertices which are not adjacent to $ v_{n-1}$ create a sub-graph $C_3$.

All vertices adjacent to $ v_{n-1}$create a sub-graph $, C_4 $. In general , $ C_{2y} $ is a graph and can be divided/ partitioned in to 2 sub graphs $ C_{2y+1}, C_{2y+2} $ .

Question:
(1) What kind of individualization is above described individualization?

(2)Is there a relation between the above individualization and k-dimensional weisfeiler lehman method?

Motivation : Graph Isomorphism.

Context: I am studying Weisfeiler Lehman method(WL method) and have clear idea about 1 and 2 dimensional WL method. I was wondering about the individualization process described below-

Defined Individualization:

$G$ is a $r$ regular graph . $n$ th vertex of $G$ is $v_n$. All vertices which are not adjacent to $ v_n $ create a sub-graph $C_1$. All vertices adjacent to $ v_n $ create a sub-graph $, C_2 $. A vertex of $C_2$ is $ v_{n-1}$.

Using same method , based on adjacency of $ v_{n-1}$, $C_2$ can be divided.

All vertices which are not adjacent to $ v_{n-1}$ create a sub-graph $C_3$.

All vertices adjacent to $ v_{n-1}$create a sub-graph $, C_4 $. In general , $ C_{2y} $ is a graph and can be divided/ partitioned in to 2 sub graphs $ C_{2y+1}, C_{2y+2} $ .

Question:
(1) What kind of individualization is above described individualization if it exists in current literature ?

(2)Is there a relation between the above individualization and k-dimensional weisfeiler lehman method?

Motivation : Graph Isomorphism.