On the unimodality of independence polynomials of some graphs
European Journal of Combinatorics
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Let P(x) be a polynomial of degree m, with nonnegative and nondecreasing coefficients. We settle the conjecture that for any positive real number d, the coefficients of P(x + d) form a unimodal sequence, of which the special case d being a positive integer has already been asserted in a previous work. Further, we explore the location of modes of P(x + d) and present some sufficient conditions on m and d for which P(x + d) has the unique mode [m-d/d+1].