Authors: YASIR BASHIR, FAISAL NADEEM, AYESHA SHABBIR
Abstract: In this paper we consider graphs in which any pair of vertices is missed by some longest path. We are proving the existence of such graphs in the infinite triangular, square and hexagonal lattices in the plane. Moreover, we extend our investigation to lattices on several surfaces such as the torus, the M\"obius strip and the Klein bottle.
Keywords: lattice graph, longest path, torus, M\"obius strip, Klein bottle
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