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 -