Hamiltonian laceability in the shadow distance graph of path graphs

P. Gomathi 1 * and R. Murali 2

doi:10.26637/MJM0701/0023

Hamiltonian laceability in the shadow distance graph of path graphs

Authors :

P. Gomathi^{1 *} and R. Murali²

Author Address :

¹Department of Mathematics, BMS College of Engineering, Bengaluru-560019, India.
²Department 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 :

10.26637/MJM0701/0023

Article Info :

Received : October 24, 2018; Accepted : January 11, 2019.