Interlace polynomials of lollipop and tadpole graphs

Abstract

In this paper, we examine interlace polynomials of lollipop and tadpole graphs. The lollipop and tadpole graphs are similar in that they both include a path attached to a graph by a single vertex. In this paper we give both explicit and recursive formulas for each graph, which extends the work of Arratia, Bollobas and Sorkin, among others. We also give special values, examine adjacency matrices and behavior of coecients of these polynomials.