Question about Vertex/Edge Sliding.

-I am editing an object in mesh mode.

-I have found that when doing vertex or edge sliding via <shift> + <lmb>
mouse button selection, and then pressing <g> + <g>, I can only
slide the [Vertex Factor] along one line and not any other lines, having
selected one vertex.

-I have also found that you can break up the mesh and only leave one line remaining.
By these means I may do vertex sliding along any other edge at all that the vertex is with.

Is there an easy way to swap a sliding vertex to another
connected line, without editing from the other side and without temporarily deleting
other edges that some vertex is part of?