On the characteristic polynomial of starlike trees

Abstract

Let A = S (m₁,⋯,m_k) and B = S (p ₁,⋯,p_k) be non-isomorphic starlike trees with characteristic polynomials and respectively. By a result of Lepović and Gutman ([5]), A and B are not coespectral and so there exists a least integer l ≥ 1 such that C_2l (A) ≠ C_2l (B). We prove in this article that l > m_u + 1, where u is the least positive integer such that m_u ≠ p_u (say m_u < p _u). In other words, we show that c_2j (A) = c_2j (B) for every 1 ≤ j ≤ m_u + 1.