Adjoint polynomials of bridgepath and bridgecycle graphs and Chebyshev polynomials

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The chromatic polynomial of a simple graph G with n>0 vertices is a polynomial Σk=1nαk(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 Σk=1nαk(Ḡ)x k, where Ḡ is the complement of G. We find explicit formulas for the adjoint polynomials of the bridgepath and bridgecycle graphs. Consequence, we find the zeros of the adjoint polynomials of several families of graphs.

Original languageEnglish
Pages (from-to)1778-1785
Number of pages8
JournalDiscrete Mathematics
Issue number16
StatePublished - 28 Aug 2011


  • Adjoint polynomial
  • Bridgegraph
  • Chebyshev polynomial

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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