A Unified Approach to the First Derivatives of Graph Polynomials

Abstract A general graph polynomial P(G, x) is introduced. It is proved that d dx P(G,x)= ∑ v∈V(G) P(G−v,x) . Special cases of this result are the previously reported first-derivative formulas for a number of graph polynomials: characteristic, matching, independence, clique polynomials, etc.