Hamiltonian Laceability in Line Graphs.

Abstract

A Connected graph G is a Hamiltonian laceable if there exists in G a Hamiltonian path between every pair of vertices in G at an odd distance. G is a Hamiltonian-t-Laceable (Hamiltoniant*- Laceable) if there exists in G a Hamiltonian path between every pair (at least one pair) of vertices at distance‘t’ in G. 1≤ t ≤ diamG. In this paper we explore the Hamiltonian-t*- laceability number ( * ) t  of graph L (G) i.e., Line Graph of G and also explore Hamiltonian-t*-Laceable of Line Graphs of Sunlet graph, Helm graph and Gear graph for t=1,2 and 3.