Abstract

We investigate number sequences that arise from counting edge covers. An edge cover is a subgraph that includes all of the original vertices, such that every vertex has degree of at least one. A tadpole graph is a cycle and a path joined at an end vertex. The number of edge covers of paths, cycles, and tadpoles have known formulas involving Fibonacci and Lucas numbers. In this project we study sequences of tadpoles joined head to tail or tail to tail. We use the Carlitz-Scoville-Vaughan theorem to find the recurrence relation for the number of edge covers.