On the Characterizing Properties of the Circuit Polynomial

E.J. Farrell 1, J.M. Guo2
1The Centre For Graph Polynomials Department of Mathematics and Computer Science The University of the West Indies St. Augustine, Trinidad
2 Department of Applied Mathematics Tongji University Shanghai, China

Abstract

It is shown that the circuit polynomial characterizes many of the well-known families of graphs. These include chains, stars, cycles, complete graphs, regular complete bipartite graphs, and wheels. Some analogous results are deduced for the characteristic polynomial and the \(\mu\)-polynomial.