# GraphTea

Your buddy to teach, learn and research on graph theory.

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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). 