1-(edge-)trail-connected square tree. (17th February 2022) - Xu, Lulu; Liu, Juan; Yang, Hong
Abstract: A graph G is s -Hamiltonian-connected if the deletion of any vertex subset with at most s vertices results in a Hamiltonian-connected graph. In this paper, for positive integer s, a graph G is s -trail-connected if for any vertex subset X with | X |≤ s, G − X is trail-connected; a graph G is s -edge-trail-connected if for any edge subset Y with| Y |≤ s, G Y is trailconnected. The main purpose of this paper is to depict the structure of 1-trail-connected and 1-edge-trail-connected square tree.