The cut-set $$\partial (S)$$ of a graph $$G=(V,E)$$ is the set edges that have one endpoint in $$S\subset V$$ and other $$V\setminus S$$ , whenever G[S] connected, cut $$[S,V\setminus S]$$ G called connected cut. A bond an inclusion-wise minimal disconnecting G, i.e., bonds are cut-sets determine cuts such $$G[V\setminus both connected. Contrasting with large number studies related to maximum c...

Recently, topology and graph theory have come together to study graphs embedded in 3-space, (see for example [1 5]). An analysis of the symmetries of spatial graphs is useful in chemistry in determining when a molecular bond graph is chiral (i.e., distinct from its mirror image). We are interested in classifying those graphs whose intrinsic structure is such that no matter how they are embedded...

In this paper, we deal with restoring missing information in molecule databases: Some data formats only store the atoms’ configuration but omit bond multiplicities. As this information is essential for various applications in chemistry, we consider the problem of recovering bond type information using a scoring function for the possible valences of each atom—the Bond Type Assignment problem. We...