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Reaction graphs and a construction of reaction networks
Authors:Jiří Pospíchal  Vladimír Kvasnička
Affiliation:(1) Department of Mathematics, Slovak Technical University, CS-81237 Bratislava, Czechoslovakia
Abstract:Summary A general definition of reaction graphs is presented. For a pair of isomeric molecular graphs 
$$mathbb{G}_1 $$
and 
$$mathbb{G}_2 $$
, related by a chemical transformation 
$$mathbb{G}_1 {text{ }} Rightarrow {text{ }}mathbb{G}_2 $$
, the reaction graph 
$$mathbb{G}_R^{{text{(}}omega {text{)}}} $$
is determined using a maximal common subgraph defined for vertex mapping 
$$omega :V(mathbb{G}_1 ) to V(mathbb{G}_2 )$$
. A binary operation lsquo oplus rsquo defined for graphs constructed over the same vertex set enables us to decompose the reaction graph 
$$mathbb{G}_R^{(omega )} $$
into the sum of prototype reaction graphs. A decomposition of an overall reaction graph can be advantageously used for the construction of a reaction network. An oriented path in this network beginning at 
$$mathbb{G}_1 $$
and ending at 
$$mathbb{G}_2 $$
corresponds to a breakdown of the transformation 
$$mathbb{G}_1 {text{ }} Rightarrow {text{ }}mathbb{G}_2 $$
into a sequence of intermediates.
Keywords:Reaction graphs  Reaction network  Graph theory
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