These look to me like basic definitions that you should be able to look up in your textbook.

The "2 sets" being the set of vertices and the set of edges between vertices.1.

A graph is defined as a pair of 2 sets. therefore operations on graphs are defined in terms of sets and set operations. Define the following operations on graph.

The graph whose vertices are precisely the vertices in the set of vertices of either of the two given graphs and whose edges are the edges in the set of edges of either of the two given graphs.1. union

The graph whose vertices are the vertices that are in sets of vertices of2. intersectionbothgiven graphs and whose edges are in the set of edges of both given graphs.

To be able to define a compliment of a set, you must have a "universal" set: a set of all things that3. complimentcanbe in a set of the type considered. In order to be able to define the compliment of a graph, you would have to have a "universal" graph: a graph that contains all possible vertices and edges. In that case the "compliment" of a graph is just the graph whose set of vertices contains all those vertices in the universal graph that arenotin the given graph and whose set of edges contains all the edges between those vertices in the universal graph.

[/quote4. decomposition[/quote]

I don't recognize this. What is the definition of a graph dividing it into two distinct graphs?

Why not the "empty" graph that has2.

in set theory we have empty set what is the analogues concept in empty set of graph theory. Find different concept for empty graph and determine the situations where each definition is suitable.novertices and no edges.