On Leaf Node Edge Switchings in Spanning Trees of De Bruijn Graphs

2018 ◽  
pp. 110-117
Author(s):  
Suman Roy ◽  
Srinivasan Krishnaswamy ◽  
P. Vinod Kumar
Keyword(s):  
Spanning Trees ◽  
Leaf Node ◽  
De Bruijn Graphs ◽  
De Bruijn

scholarly journals An Algebraic Analogue of a Formula of Knuth

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Lionel Levine
Keyword(s):  
Directed Graph ◽  
Spanning Trees ◽  
Line Graph ◽  
Torsion Subgroup ◽  
Directed Line ◽  
De Bruijn Graphs ◽  
International Audience ◽  
De Bruijn ◽  
Kautz Graphs ◽  
Sandpile Group

International audience We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph $G$ and its directed line graph $\mathcal{L} G$. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted at a fixed vertex. In the case when $G$ is regular of degree $k$, we show that the sandpile group of $G$ is isomorphic to the quotient of the sandpile group of $\mathcal{L} G$ by its $k$-torsion subgroup. As a corollary we compute the sandpile groups of two families of graphs widely studied in computer science, the de Bruijn graphs and Kautz graphs. Nous généralisons un théorème de Knuth qui relie les arbres couvrants dirigés d'un graphe orienté $G$ au graphe adjoint orienté $\mathcal{L} G$. On peut associer à tout graphe orienté un groupe abélien appelé groupe du tas de sable, et dont l'ordre est le nombre d'arbres couvrants dirigés enracinés en un sommet fixé. Lorsque $G$ est régulier de degré $k$, nous montrons que le groupe du tas de sable de $G$ est isomorphe au quotient du groupe du tas de sable de $\mathcal{L} G$ par son sous-groupe de $k$-torsion. Comme corollaire, nous déterminons les groupes de tas de sable de deux familles de graphes étudiées en informatique: les graphes de de Bruijn et les graphes de Kautz.

A Bijective Proof of a Theorem of Knuth

2010 ◽  
Vol 20 (1) ◽  
pp. 11-25 ◽  
Author(s):  
HODA BIDKHORI ◽  
SHAUNAK KISHORE
Keyword(s):  
Spanning Trees ◽  
Line Graph ◽  
Binary Sequences ◽  
Critical Groups ◽  
De Bruijn Graphs ◽  
Bijective Proof ◽  
The Matrix ◽  
De Bruijn ◽  
Kautz Graphs ◽  
Number Of Spanning Trees

The line graph G of a directed graph G has a vertex for every edge of G and an edge for every path of length 2 in G. In 1967, Knuth used the Matrix Tree Theorem to prove a formula for the number of spanning trees of G, and he asked for a bijective proof [6]. In this paper, we give a bijective proof of Knuth's formula. As a result of this proof, we find a bijection between binary de Bruijn sequences of degree n and binary sequences of length 2n−1. Finally, we determine the critical groups of all the Kautz graphs and de Bruijn graphs, generalizing a result of Levine [7].

scholarly journals Buffering Updates Enables Efficient Dynamic de Bruijn Graphs

2021 ◽  
Author(s):  
Jarno Alanko ◽  
Bahar Alipanahi ◽  
Jonathen Settle ◽  
Christina Boucher ◽  
Travis Gagie
Keyword(s):  
De Bruijn Graphs ◽  
De Bruijn

scholarly journals Matching preclusion and conditional edge-fault Hamiltonicity of binary de Bruijn graphs

2017 ◽  
Vol 233 ◽  
pp. 104-117 ◽  
Author(s):  
Ruizhi Lin ◽  
Heping Zhang
Keyword(s):  
De Bruijn Graphs ◽  
De Bruijn

scholarly journals Cartesian products of graphs as subgraphs of de Bruijn graphs of dimension at least three

1997 ◽  
Vol 79 (1-3) ◽  
pp. 3-34 ◽  
Author(s):  
Thomas Andreae ◽  
Martin Hintz ◽  
Michael Nölle ◽  
Gerald Schreiber ◽  
Gerald W. Schuster ◽  
...  
Keyword(s):  
Cartesian Products ◽  
De Bruijn Graphs ◽  
De Bruijn ◽  
Cartesian Products Of Graphs

scholarly journals Integrating long-range connectivity information into de Bruijn graphs

2018 ◽  
Vol 34 (15) ◽  
pp. 2556-2565 ◽  
Author(s):  
Isaac Turner ◽  
Kiran V Garimella ◽  
Zamin Iqbal ◽  
Gil McVean
Keyword(s):  
Long Range ◽  
De Bruijn Graphs ◽  
Connectivity Information ◽  
De Bruijn
Sign in / Sign up

Export Citation Format

Share Document