The factorial representation of balanced labelled graphs

AbstractAn important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.

Download Full-text

Combinatorial entanglement: detecting entanglement in quantum states using grid-labelled graphs

Electronic Notes in Discrete Mathematics ◽

10.1016/j.endm.2017.07.041 ◽

2017 ◽

Vol 61 ◽

pp. 819-825 ◽

Cited By ~ 1

Author(s):

Joshua Lockhart ◽

Otfried Gühne ◽

Simone Severini

Keyword(s):

Quantum States ◽

Labelled Graphs

Download Full-text

Algorithms for generating labelled graphs with given degree

Journal of Computational and Applied Mathematics ◽

10.1016/0377-0427(91)90117-3 ◽

1991 ◽

Vol 37 (1-3) ◽

pp. 187-194 ◽

Cited By ~ 1

Author(s):

V. Fack ◽

J. Van der Jeugt

Keyword(s):

Labelled Graphs

Download Full-text

A Variational Model on Labelled Graphs with Cusps and Crossings

Computational Imaging and Vision - Shape Reconstruction from Apparent Contours ◽

10.1007/978-3-662-45191-5_1 ◽

2015 ◽

pp. 1-24 ◽

Cited By ~ 1

Author(s):

Giovanni Bellettini ◽

Valentina Beorchia ◽

Maurizio Paolini ◽

Franco Pasquarelli

Keyword(s):

Variational Model ◽

Labelled Graphs

Download Full-text

Random Graphs from a Minor-Closed Class

Combinatorics Probability Computing ◽

10.1017/s0963548309009717 ◽

2009 ◽

Vol 18 (4) ◽

pp. 583-599 ◽

Cited By ~ 20

Author(s):

COLIN McDIARMID

Keyword(s):

Poisson Distribution ◽

Random Graph ◽

Generating Function ◽

Random Graphs ◽

Giant Component ◽

Closed Class ◽

Exponential Generating Function ◽

Excluded Minor ◽

A Minor ◽

Labelled Graphs

A minor-closed class of graphs is addable if each excluded minor is 2-connected. We see that such a classof labelled graphs has smooth growth; and, for the random graphRnsampled uniformly from then-vertex graphs in, the fragment not in the giant component asymptotically has a simple ‘Boltzmann Poisson distribution’. In particular, asn→ ∞ the probability thatRnis connected tends to 1/A(ρ), whereA(x) is the exponential generating function forand ρ is its radius of convergence.

Download Full-text