Permutation-partition pairs. III. Embedding distributions of linear families of graphs

AbstractFor any fixed graph H, and H-linear family of graphs is a sequence {Gn}n=1∞ of graphs in which Gn consists of n copies of H that have been linked in a consistent manner so as to form a chain. Generating functions for the region distribution of any such family are found. It is also shown that the minimum genus and the average genus of Gn are essentially linear functions of n