BUILT-IN MATHEMATICA SYMBOL

BooleanGraph

gives the Boolean graph defined by the Boolean function bfunc on the graphs

, ...,

.

An edge is in the resulting graph if bfunc[EdgeQ[g₁, uv], ..., EdgeQ[g_n, uv]] is True.

An edge is in the resulting graph if bfunc[EdgeQ[g_i, uv], ..., EdgeQ[g_n, uv]] is True.

The Boolean combination of two graphs:

Out[1]=

Out[2]=

BooleanGraph works with undirected graphs:

Directed graphs:

BooleanGraph works with as many graphs as the Boolean function:

Define the symmetric graph difference Xor:

Convert the Boolean expression Xor to disjunctive normal form:

Implement it by related functions:

Compare to the result by using Xor directly:

Define the graph Nand:

Convert the Boolean expression Nand to disjunctive normal form:

Implement it by related functions:

Compare to the result by using Nand directly:

Define the graph Nor:

Convert the Boolean expression Nor to disjunctive normal form:

Implement it by related functions:

Compare to the result by using Nor directly:

Compute the Boolean graph for all Boolean functions of two variables:

Use BooleanFunction to enumerate all Boolean functions of two variables:

Compute the Boolean graph using these functions:

GraphUnion corresponds to Or:

BooleanGraph does not necessarily produce simple graphs:

Use SimpleGraph if only a simple graph is needed: