Laceability on a class of line graph of cartesian product of graphs

Abstract

Determining Hamiltonian path connectivity relationship among the nodes of the network increases its optimal connectivity. If a and b are nodes in a graph G so that d(a,b) = t and then P is a non-Hamilton path in G. G is referred to as K + r hypo -edge -Hamilton-t -laceable if P + re forms Hamilton path joining a and b, for each t for 1 ⩽ t ⩽ diamG. In this research article we investigate the hypo-edge-Hamilton laceability of line graph of Cartesian product of paths and cycles. Also we discuss the results on Cartesian product of path and wheel.