On upper bounds and connectivity of cages

In this talk we exhibit new upper bounds for the order of (k,g)-cages when k−1 is not a prime power and g∈{6,8,12}. As an application we obtain new upper bounds for the order of cages when g=11 and g=12 and k−1 is not a prime power. We also confirm a conjecture of Fu, Huang and Rodger on the k-connectivity of (k,g)-cages for g=12, and for g={7,11} when k−1 is a prime power.