Monotonicity of the order of (D;g)(D;g)-cages

A (D;g)(D;g)-cage is a graph having degree set DD, girth gg, and the minimum possible number of vertices, which is denoted by n(D;g)n(D;g). When D={r}D={r} the corresponding ({r};g)({r};g)-cage is clearly rr-regular, and is called an (r;g)(r;g)-cage. In this work we prove that if g