Let's say we have two matrices $M$ and $G$ with $G, M \in \{0, 1\}^{n, n}$, we denote by $m\_{i, j}$ the element of $M$ in the $i^\text{th}$ row and $j^\text{th}$ column, same for $G\_{i, j}$.


Let's define $K$ the matrix resulting from the matrix operation $G \oplus M$ as follows:


$$\forall i, j \in [1\ldots n] \ \ K\_{i,j} = \bigvee\_{k \in [1\ldots n]} m\_{i,k} \wedge G\_{k,j}.$$


I know this operation has a name as it is used in graph theory; however I don't remember what it was. Does someone know the name of this operation?



What is the name of a matrix operation using the OR operator instead of addition?
Your operation is known as Boolean matrix multiplication. There is a considerable literature on efficient algorithms; see for example [An improved combinatorial algorithm for Boolean matrix multiplication](https://doi.org/10.1016/j.ic.2018.02.006) by Huacheng Yu.


