TRIANGLE GRAPHS

We introduce a new class of planar graphs called triangle graphs. Firs t, we present a formal way of constructing and characterizing triangle graphs, and then show that they characterize the adjacencies of arbit rary triangulations and they are three-colorable for a certain subclas s of triangulations. Subsequently, we discuss an application of triang le graphs to the parallel finite element solution of elliptic partial differential equations on triangulated domains.