Adjoint polynomials of bridge-path and bridge-cycle graphs and Chebyshev polynomials

Abstract

The chromatic polynomial of a simple graph G with n > 0 vertices is a polynomial ∑n k=1 αk(G)x(x− 1) · · · (x−k+1) of degree n, where αk(G) is the number of k-independent partitions of G for all k. The adjoint polynomial of G is defined to be ∑n k=1 αk(G)x , where G is the complement of G. We find explicit formulas for the adjoint polynomials of the bridge… (More)
DOI: 10.1016/j.disc.2011.04.022

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