The Study of Intersection Graphs Was Started In the Early1950's. Chordal Graphs Are Very Important Type of Intersection Graphs. a Major Investigation of Chordalgraph: Under the Frame Work of Intersection Graphs Was Done By Gavril . It Wasgavril Who Proved the Very Important Result That Chordal Graphs Areintersection Graphs of Subtrees of a Tree. Interval Graphs and Circular Arcgraphs Are Very Important Types of Subtree Graphs and Were Studied By Gilmoreand Hoffman.