| dc.description.abstract | Mathematical trees are connected graphs without cycles, loops and multiple edges. Various trees such as Cayley
trees, plane trees, binary trees, d-ary trees, noncrossing trees among others have been studied extensively.
Tree-like structures such as Husimi graphs and cacti are graphs which posses the conditions for trees if, instead
of vertices, we consider their blocks. In this paper, we use generating functions and bijections to find formulas for
the number of noncrossing Husimi graphs, noncrossing cacti and noncrossing oriented cacti. We extend the
work to obtain formulas for the number of bicoloured noncrossing Husimi graphs, bicoloured noncrossing cacti
and bicoloured noncrossing oriented cacti. Finally, we enumerate plane Husimi graphs, plane cacti and plane
oriented cacti according to number of blocks, block types and leaves | en_US |
