Research output: Contribution to journal › Article › peer-review
The Generating Function is Rational for the Number of Rooted Forests in a Circulant Graph. / Kamalov, U. P.; Kutbaev, A. B.; Mednykh, A. D.
In: Siberian Advances in Mathematics, Vol. 33, No. 4, 12.2023, p. 322-328.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - The Generating Function is Rational for the Number of Rooted Forests in a Circulant Graph
AU - Kamalov, U. P.
AU - Kutbaev, A. B.
AU - Mednykh, A. D.
N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0005). Публикация для корректировки.
PY - 2023/12
Y1 - 2023/12
N2 - We consider the generating function Φ for the number fΓ(n) of rooted spanning forests in the circulant graph Γ , where Φ(x) =∑∞n=1fΓ(n)xn and either Γ=Cn(s1,s2,..,sk) or Γ=C2n(s1,s2,..,sk,.n) . We show that Φ is a rational function with integer coefficients thatsatisfies the condition Φ(x) = −Φ(1/x). . We illustrate this result by a series of examples.
AB - We consider the generating function Φ for the number fΓ(n) of rooted spanning forests in the circulant graph Γ , where Φ(x) =∑∞n=1fΓ(n)xn and either Γ=Cn(s1,s2,..,sk) or Γ=C2n(s1,s2,..,sk,.n) . We show that Φ is a rational function with integer coefficients thatsatisfies the condition Φ(x) = −Φ(1/x). . We illustrate this result by a series of examples.
KW - circulant graph
KW - generating function
KW - rooted spanning forest
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85179710615&origin=inward&txGid=f6ae250175151791c7573effc243184d
UR - https://www.mendeley.com/catalogue/578fd2eb-81f2-31e7-bd9a-20fddb496cfc/
U2 - 10.1134/S1055134423040041
DO - 10.1134/S1055134423040041
M3 - Article
VL - 33
SP - 322
EP - 328
JO - Siberian Advances in Mathematics
JF - Siberian Advances in Mathematics
SN - 1055-1344
IS - 4
ER -
ID: 59542893