**Possible graph operations in GraphTea:**

Thsese operations can be found under the menu "Operations".

You can also execute them by using GraphTea shell and run the

specific command which we mentioned below.

**Cartesian Product** (GraphTea Command: cartesian_produce)

The Cartesian product of two graphs G and H is the graph with the vertex set V(G) x V(H) in which (g1,h1) is adjacent with (g2,h2) if and only if

- g1=g2 and h1 is adjancent with h2 or
- h1=h2 and g1 is adjacent with g2

**Tensor Product** (GraphTea Command: tensor_product)

The Tensor product of two graphs G and H is the graph with the vertex set V(G) x V(H) in which (g1,h1) is adjacent with (g2,h2) if and only if g1 is adjacent with g2 and h1 is adjacent with h2.

**Disjunction **(GraphTea Command: gdisjunction)

The disjunction of two graphs G and H is the graph with vertex set V(G) x V (H) in which (g1, h1) is adjacent with (g2, h2) whenever g1 is adjacent with g2 or h1 is adjacent with h2 in H.

**Symmetric Difference** (GraphTea Command: gsymdiff)

The symmetric difference of two graphs G and H is the graph with vertex set V (G) x V (H) in which (g1, h1) is adjacent with (g2, h2) whenever g1 is adjacent with g2 in G or h1 is adjacent with h2 in H, but not both.

**Composition** (GraphTea Command: gcomposition)

The composition G[H] of graphs G and H with disjoint vertex sets and edge sets is again a graph on vertex set V (G) * V (H) in which (g1, h1) is adjacent with (g2, h1) whenever g1 is adjacent with g2 or g1 = g2 and h1 adjacent with h2.

**Sum** (GraphTea Command: gsum)

Let G and H be two graphs on disjoint vertex sets. Their sum is the graph G + H on the vertex set V (G) U V (H) and the edge set E (G + H) = E (G) U E (H) U {{g, h}; g in V (G) , h in V (H)}.

**Corona Product** (GraphTea Command: gcorona)

For G and H we define their corona product as the graph obtained by taking |V (G)| copies of H and joining each vertex of the i-th copy with vertex vi in V (G).