The number of quasi-trees in fans and wheels
The electronic journal of combinatorics, Tome 30 (2023) no. 1
We extend the classical relation between the $2n$-th Fibonacci number and the number of spanning trees of the $n$-fan graph to ribbon graphs. More importantly, we establish a relation between the $n$-associated Mersenne number and the number of quasi trees of the $n$-wheel ribbon graph. The calculations are performed by computing the determinant of a matrix associated with ribbon graphs. These theorems are also proven using contraction and deletion in ribbon graphs. The results provide neat and symmetric combinatorial interpretations of these well-known sequences. Furthermore, they are refined by giving two families of abelian groups whose orders are the Fibonacci and associated Mersenne numbers.
DOI :
10.37236/11097
Classification :
05C30, 05C10, 11B39
Mots-clés : Fibonacci number, \(n\)-wheel ribbon graph
Mots-clés : Fibonacci number, \(n\)-wheel ribbon graph
Affiliations des auteurs :
Criel Merino 1
@article{10_37236_11097,
author = {Criel Merino},
title = {The number of quasi-trees in fans and wheels},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {1},
doi = {10.37236/11097},
zbl = {1510.05118},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11097/}
}
Criel Merino. The number of quasi-trees in fans and wheels. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11097
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