On the characteristic polynomial of starlike trees

Abstract:

Let A = S (m<inf>1</inf>,⋯,m<inf>k</inf>) and B = S (p <inf>1</inf>,⋯,p<inf>k</inf>) 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<inf>2l</inf> (A) ≠ C<inf>2l</inf> (B). We prove in this article that l > m<inf>u</inf> + 1, where u is the least positive integer such that m<inf>u</inf> ≠ p<inf>u</inf> (say m<inf>u</inf> < p <inf>u</inf>). In other words, we show that c<inf>2j</inf> (A) = c<inf>2j</inf> (B) for every 1 ≤ j ≤ m<inf>u</inf> + 1.

Año de publicación:

2009

Keywords:

Fuente:

scopus

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