Line triangle intersection graph

Abstract

A graph operator is a mapping between two families of graphs. In this paper, a new graph operator called the line triangle intersection graph is introduced. Also, the concept of a quasi regular graph is proposed. Further, various properties of line triangle intersection graph of a graph are investigated including its chromatic number and clique number. It is proved that the line triangle intersection graph of a complete graph is quasi regular. Moreover, partial characterization for a line triangle intersection graph is presented.