Intersection graph :- An intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph may be represented as an intersection graph, but some important special classes of graphs may be defined by the types of sets that are used to form an intersection representation of them.For an overview of the theory of intersection graphs, and of important special classes of intersection graphs. Interval graph :- An Interval graph is the intersection graph of a multiset of intervals on the real line. It has one vertex for each interval in the set, and an edge between every pair of vertices corresponding to intervals that intersect. The mathematical theory of interval graphs was developed with a view towards applications by researchers at the RAND Corporation's mathematics department, which included young researchers—such as Peter C. Fishburn and students like Alan C. Tucker and Joel E. Cohen—besides leaders—such as Delbert Fulkerson and (recurring visitor) Victor Klee.[7] Cohen applied interval graphs to mathematical models of population biology, specifically food webs. Types of vertices In graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be the endpoints of this, and the edge is said to be incident to the vertices. A vertex w is said to be adjacent to another vertex v if the graph contains an edge (v,w). The neighborhood of a vertex v is an induced subgraph of the graph, formed by all vertices adjacent to v. The degree of a vertex in a graph is the number of edges incident to it. An isolated vertex is a vertex with degree zero; that is, a vertex that is not an endpoint of any edge. A leaf vertex (also pendant vertex) is a vertex with degree one. In a directed graph, one can distinguish the outdegree (number of outgoing edges) from the indegree (number of incoming edges); a source vertex is a vertex with indegree zero, while a sink vertex is a vertex with outdegree zero. Read More About :- Real Numbers chart
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