Hamiltonian laceability in the shadow distance graph of path graphs
Authors :
P. Gomathi 1 * and R. Murali 2
Author Address :
1 Department of Mathematics, BMS College of Engineering, Bengaluru-560019, India.
2 Department of Mathematics, Dr. Ambedkar Institute of Technology, Bengaluru-560056, India.
*Corresponding author.
Abstract :
A connected graph $G$ is termed hamiltonian-$t$-laceable ($t$*-laceable) if there exists in it a hamiltonian path between every pair (at least one pair) of distinct vertices $u$ and $v$ with the property $d(u, v) = t, 1leq t leq diam(G)$, where $t$ is a positive integer. In this paper, we establish laceability properties in the edge tolerant shadow distance graph of the path graph $P_n$ with distance set $D_s={1,2k}$.
Keywords :
Hamiltonian laceable, hamiltonian-$t$-laceable, hamiltonian-$t^*$-laceable, shadow graph, shadow distance graph.
DOI :
Article Info :
Received : October 24, 2018; Accepted : January 11, 2019.