The graph sum of graphs 
and 
is the graph with adjacency
matrix given by the sum of adjacency matrices of 
and 
.
A graph sum is defined when the orders of 
and 
are the same. The example illustrated above shows the graph sum 
of the pentatope graph 
and the cycle
graph 
,
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].](/images/equations/GraphSum/NumberedEquation1.svg) |
Graph sums can be computed in the Wolfram Language using GraphSum[g, h].
