New infinite family of regular edge-isoperimetric graphs

We introduce a new infinite family of regular graphs admitting nested solutions in the edge-isoperimetric problem for all their Cartesian powers. The obtained results include as special cases most of previously known results in this area

A Note on Edge Isoperimetric Numbers and Regular Graphs

This note resolves an open problem asked by Bezrukov in the open problem session of IWOCA 2014. It shows an equivalence between regular graphs and graphs for which a sequence of invariants presents some symmetric property. We extend this result to a few other sequences. © 2016 World Scientific Publishing Company