The graph sum of graphs G and H is the graph with adjacency matrix given by the sum of adjacency matrices of G and H. A graph sum is defined when the orders of G and H are the same. The example illustrated above shows the graph sum K_5 + C_5 of the pentatope graph K_5 and the cycle graph C_5, corresponding to adjacency matrices [0 | 1 | 1 | 1 | 1 1 | 0 | 1 | 1 | 1 1 | 1 | 0 | 1 | 1 1 | 1 | 1 | 0 | 1 1 | 1 | 1 | 1 | 0] + [0 | 1 | 0 | 0 | 1 1 | 0 | 1 | 0 | 0 0 | 1 | 0 | 1 | 0 0 | 0 | 1 | 0 | 1 1 | 0 | 0 | 1 | 0] = [0 | 2 | 1 | 1 | 2 2 | 0 | 2 | 1 | 1 1 | 2 | 0 | 2 | 1 1 | 1 | 2 | 0 | 2 2 | 1 | 1 | 2 | 0]. Graph sums can be computed in the Wolfram Language using GraphSum[g, h].

graph difference | graph join | graph union

GraphSum