On sigma-polynomials and a class of chromatically unique graphs

Abstract Let σ( G )=∑ k i =0 a i σ k − i be the σ-polynomial of a graph G . We ask the question: When k and a 1 are given, what is the largest possible value of a i (0⩽ i ⩽ k ) for any graph G ? In this paper, this question is answered and the extremal graphs are characterized. So, the results in [3,6] are generalized.

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