No 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.

A simple connected graph is known to be Hamiltonian-t-laceable if there will be a Hamiltonian path between each pair of distinct vertices at a distance ‘t’ in G where t ∈ Z + such that 1 ≤ t ≤ diam(G). In this paper we define M-flower snark graph and discuss the hypo edge Hamiltonian laceability properties in M-flower snark graphs and Cartesian product graphs.