Extending a conjecture of Graham and Lovász on the distance characteristic polynomial

Aida Abiad; Boris Brimkov; Sakander Hayat; Antonina P. Khramova; Jack H. Koolen

doi:10.1016/j.laa.2023.03.027

Extending a conjecture of Graham and Lovász on the distance characteristic polynomial

Aida Abiad (Corresponding author), Boris Brimkov, Sakander Hayat, Antonina P. Khramova, Jack H. Koolen

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order n is unimodal with the maximum value occurring at [Formula presented]. In this paper we investigate this problem for block graphs. In particular, we prove the unimodality part and we establish the peak for several extremal cases of uniform block graphs with small diameter.

Originele taal-2	Engels
Pagina's (van-tot)	63-82
Aantal pagina's	20
Tijdschrift	Linear Algebra and Its Applications
Volume	693
DOI's	https://doi.org/10.1016/j.laa.2023.03.027
Status	Gepubliceerd - 15 jul. 2024

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abstract = "Graham and Lov{\'a}sz conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order n is unimodal with the maximum value occurring at [Formula presented]. In this paper we investigate this problem for block graphs. In particular, we prove the unimodality part and we establish the peak for several extremal cases of uniform block graphs with small diameter.",

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AU - Abiad, Aida

AU - Brimkov, Boris

AU - Hayat, Sakander

AU - Khramova, Antonina P.

AU - Koolen, Jack H.

PY - 2024/7/15

Y1 - 2024/7/15

N2 - Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order n is unimodal with the maximum value occurring at [Formula presented]. In this paper we investigate this problem for block graphs. In particular, we prove the unimodality part and we establish the peak for several extremal cases of uniform block graphs with small diameter.

AB - Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order n is unimodal with the maximum value occurring at [Formula presented]. In this paper we investigate this problem for block graphs. In particular, we prove the unimodality part and we establish the peak for several extremal cases of uniform block graphs with small diameter.

KW - Block graph

KW - Characteristic polynomial

KW - Distance matrix

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U2 - 10.1016/j.laa.2023.03.027

DO - 10.1016/j.laa.2023.03.027

M3 - Article

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VL - 693

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EP - 82

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Extending a conjecture of Graham and Lovász on the distance characteristic polynomial

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