On Hamilton Laceability and Random Hamiltonian-t*– Laceablity of Total Transformation Graph G-++
Nagarathnamma K. G.1,3, Leena N. Shenoy2,3
1Assistant Professor, Department of Mathematics, Dayananda Sagar college of Engineering, Bengaluru-560078, India
2Associate Professor, Department of Mathematics, B.N.M. Institute of Technology, Bengaluru-560070, India
3Visveswaraya Technological University, Belagavi-590018, India
Abstract: A connected graph G = (V, E) is called Hamiltonian if G contains a spanning cycle and if a graph G 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 G is random Hamiltonian- t* – laceable if there exists a u – v Hamiltonian path for at least one pair u, v ɛ V(G) for t* distance. In this paper, we have studied the Hamiltonian laceble and random Hamiltonian-t*– laceable graphs of total transformation graph G-++ of graphs viz. path Pn, cycle Cn, complete bipartite graph K, n-dimensional convex polytopes Dn, Hn and Gn.
Keywords: Hamiltonian graph, Hamiltonian connected, Hamilton-laceable, total transformation graph.