TY - JOUR

T1 - Counting spanning trees in cobordism of two circulant graphs

AU - Baigonakova, Galya Amanboldynovna

AU - Mednykh, Ilya Aleksandrovich

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We consider a family of graphs Hn(s1, ..., sk; t1, ..., tl) that is a generalisation of the family of I-graphs, which, in turn, includes the generalized Petersen graphs. We present an explicit formula for the number τ(n) of spanning trees in these graphs in terms of the Chebyshev polynomials and find its asymptotics. Also, we show that the number of spanning trees can be represented in the form τ(n) = p n a(n)2; where a(n) is an integer sequence and p is a prescribed integer depending on the number of even elements in the sequence s1, ..., sk; t1, ..., tl and the parity of n.

AB - We consider a family of graphs Hn(s1, ..., sk; t1, ..., tl) that is a generalisation of the family of I-graphs, which, in turn, includes the generalized Petersen graphs. We present an explicit formula for the number τ(n) of spanning trees in these graphs in terms of the Chebyshev polynomials and find its asymptotics. Also, we show that the number of spanning trees can be represented in the form τ(n) = p n a(n)2; where a(n) is an integer sequence and p is a prescribed integer depending on the number of even elements in the sequence s1, ..., sk; t1, ..., tl and the parity of n.

KW - Chebyshev polynomial

KW - Circulant graph

KW - I-graph

KW - Mahler measure

KW - Petersen graph

KW - Spanning tree

KW - I-GRAPHS

KW - NUMBER

KW - spanning tree

KW - COMPLEXITY

KW - circulant graph

KW - FORMULAS

UR - http://www.scopus.com/inward/record.url?scp=85069981202&partnerID=8YFLogxK

U2 - 10.17377/semi.2018.15.093

DO - 10.17377/semi.2018.15.093

M3 - Article

AN - SCOPUS:85069981202

VL - 15

SP - 1145

EP - 1157

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -