Extending a conjecture of Graham and Lovász on the distance characteristic polynomial
نویسندگان
چکیده
Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients distance characteristic polynomial a tree order n is unimodal with maximum value occurring at ⌊n2⌋. In this paper we investigate problem for block graphs. particular, prove unimodality part establish peak several extremal cases uniform graphs small diameter.
منابع مشابه
On a conjecture of Graham and Lovász about distance matrices
In their 1978 paper \Distance Matrix Polynomials of Trees", [4], Graham and Lov asz proved that the coeÆcients of the characteristic polynomial of the distance matrix of a tree (CPD(T )) can be expressed in terms of the numbers of certain subforests of the tree. This result was generalized to trees with weighted edges by Collins, [1], in 1986. Graham and Lov asz computed these coeÆcients for al...
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We establish a conjecture of Graham and Lovász that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal; we also prove they are log-concave. Email addresses: [email protected] (Ghodratollah Aalipour), [email protected] (Aida Abiad), [email protected] (Zhanar Berikkyzy), [email protected] (Leslie Hogben), [email protected] (Fra...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2023
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2023.03.027