A k-tree is a chordal graph all of whose maximal cliques are the same size k + 1 and all of whose minimal clique separators are also all the same size k. If a 3-Tree chordal graph G has a planar embedding, then it is called as planar 3-Trees. A planar graph is a graph that can be embedded in the plane. Given a chordal 3-tree G , compute an embedding on the plane without edge crossings. In this work, we investigate local properties that provide information about the global cycle structure of a

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... aph. There exists a closed walk on the graph along the edges such that visited each vertex exactly once and cover all the vertices in a single closed walk. We present a linear time algorithm to characterize the Hamiltonianicity of a 3-tree, and polynomial time algorithm to recognize the Hamiltonian circuit in the planar 3-tree. We begin by defining the global cycle properties that we shall consider. The order (number of vertices) of a graph G is denoted by n. A graph G is Hamiltonian if G has a cycle of length n. We emulate flexibility and feasibility by giving more features into the UI. Primary objective is to establish a structural properties and characterization of planar 3-trees and Hamiltonian cycle. Hamiltonian cycle has more characterization on planar 3-trees with respect to simplicial ordering and perfect elimination ordering.