### Abstract

A reaction-pathway identification procedure has two distinct phases. The first phase enumerates exhaustively the feasible candidate pathways, and the second phase identifies the ultimate feasible pathway or pathways among them. Probably the most efficient way to execute the first phase is to algorithmically generate the networks of feasible candidate pathways from a predefined set of plausible elementary reactions. The available algorithmic methods for this purpose can be roughly grouped into two major classes, one based on graph theory and the other on linear algebra. Both classes of methods consider any chemical reaction system as a network of elementary reactions, thereby implying that the two classes are interrelated. This paper studies the linear algebraic concept termed direct mechanism introduced in the mid-eighties and the graph-theoretical concept termed structurally minimal pathway introduced two decades later. Herein, it has been formally proven that the two concepts are equivalent.

Original language | English |
---|---|

Pages (from-to) | 1347-1361 |

Number of pages | 15 |

Journal | Journal of Mathematical Chemistry |

Volume | 50 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2012 |

### Fingerprint

### Keywords

- Graph theory
- Linear algebra
- Mechanism
- Pathway

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*50*(5), 1347-1361. https://doi.org/10.1007/s10910-012-9974-0

**On the equivalence of direct mechanisms and structurally minimal pathways.** / Barany, Mate; Bertók, B.; Imreh, Csanad; Fan, L. T.; Friedler, F.

Research output: Contribution to journal › Article

*Journal of Mathematical Chemistry*, vol. 50, no. 5, pp. 1347-1361. https://doi.org/10.1007/s10910-012-9974-0

}

TY - JOUR

T1 - On the equivalence of direct mechanisms and structurally minimal pathways

AU - Barany, Mate

AU - Bertók, B.

AU - Imreh, Csanad

AU - Fan, L. T.

AU - Friedler, F.

PY - 2012/5

Y1 - 2012/5

N2 - A reaction-pathway identification procedure has two distinct phases. The first phase enumerates exhaustively the feasible candidate pathways, and the second phase identifies the ultimate feasible pathway or pathways among them. Probably the most efficient way to execute the first phase is to algorithmically generate the networks of feasible candidate pathways from a predefined set of plausible elementary reactions. The available algorithmic methods for this purpose can be roughly grouped into two major classes, one based on graph theory and the other on linear algebra. Both classes of methods consider any chemical reaction system as a network of elementary reactions, thereby implying that the two classes are interrelated. This paper studies the linear algebraic concept termed direct mechanism introduced in the mid-eighties and the graph-theoretical concept termed structurally minimal pathway introduced two decades later. Herein, it has been formally proven that the two concepts are equivalent.

AB - A reaction-pathway identification procedure has two distinct phases. The first phase enumerates exhaustively the feasible candidate pathways, and the second phase identifies the ultimate feasible pathway or pathways among them. Probably the most efficient way to execute the first phase is to algorithmically generate the networks of feasible candidate pathways from a predefined set of plausible elementary reactions. The available algorithmic methods for this purpose can be roughly grouped into two major classes, one based on graph theory and the other on linear algebra. Both classes of methods consider any chemical reaction system as a network of elementary reactions, thereby implying that the two classes are interrelated. This paper studies the linear algebraic concept termed direct mechanism introduced in the mid-eighties and the graph-theoretical concept termed structurally minimal pathway introduced two decades later. Herein, it has been formally proven that the two concepts are equivalent.

KW - Graph theory

KW - Linear algebra

KW - Mechanism

KW - Pathway

UR - http://www.scopus.com/inward/record.url?scp=84862188966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862188966&partnerID=8YFLogxK

U2 - 10.1007/s10910-012-9974-0

DO - 10.1007/s10910-012-9974-0

M3 - Article

VL - 50

SP - 1347

EP - 1361

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 5

ER -