A Note on the Pancyclism of Block Intersection Graphs for Universal Friendship Hypergraphs

In this note, we consider the $i$-block intersection graphs ($i$-BIG) of a universal friendship $3$-hypergraph and show that they are pancyclic for $i = 1,2$. We also show that the $1$-BIG of a universal friendship $3$-hypergraph is Hamiltonian-connected.