Abstract:
For every integer
4\leq d \leq 11 
, an explicit construction of infinite families of
2d
-regular unique-neighbor expanders is presented, which is a generalization of the 6-regular unique-neighbors initially developed by Alon and Capalbo. Additionally, for values of
d
greater than 11, a sufficient condition is established for employing the same construction method. Our construction method involves the “line product” of large bipartite Ramanujan graphs and a sufficiently good unique-neighbor expander (a small gadget).