On Hamilton Laceability and Random Hamiltonian-t*– Laceablity of Total Transformation Graph G-++

A connected graph is called Hamiltonian if contains a spanning cycle and if a graph contains a spanning path between arbitrary pair of its vertices is called Hamilton-connected. A bipartite graph is called Hamilton-laceable if there exist Hamiltonian path between vertices of different partite sets and a graph is random Hamiltonian-– laceable if there exists a Hamiltonian path for at least one pair for distance. In this paper, we have studied the Hamiltonian laceble and random Hamiltonian-– laceable graphs of total transformation graph of graphs viz. path , cycle , complete bipartite graph , n-dimensional convex polytopes , and gn .