Let 2 <= r < m and g be positive integers. An ({r, m}; g)-graph (or biregular graph) is a graph with degree set {r, m} and girth g, and an ({r, m}; g)-cage (or biregular cage) is an ({r, m}; g)-graph of minimum order n({r, m}; g). If m = r +1, an ({r,m};g)-cage is said to be a semiregular cage.
In this paper we generalize the reduction and graph amalgam operations from [M. Abreu, G. Araujo Pardo, C. Balbuena, D. Labbate. Families of Small Regular Graphs of Girth 5. Discrete Math. 312(18) (2012)...
Let 2 <= r < m and g be positive integers. An ({r, m}; g)-graph (or biregular graph) is a graph with degree set {r, m} and girth g, and an ({r, m}; g)-cage (or biregular cage) is an ({r, m}; g)-graph of minimum order n({r, m}; g). If m = r +1, an ({r,m};g)-cage is said to be a semiregular cage.
In this paper we generalize the reduction and graph amalgam operations from [M. Abreu, G. Araujo Pardo, C. Balbuena, D. Labbate. Families of Small Regular Graphs of Girth 5. Discrete Math. 312(18) (2012) 2832-2842] on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. The constructed new families are ({r, 2r - 3}; 5)-cages for all r = q + 1 with q a prime power, and ({r, 2r - 5}; 5)-cages for all r = q + 1 with q a prime. The new semiregular cages are constructed for r = 5 and 6 with 31 and 43 vertices respectively.