A novel nomenclature of polycyclic aromatic hydrocarbons without using graph centre

In this paper, we develop a novel adjacency matrix, He-matrix, corresponding to the dualist graph. Without using the graph center concept, we advance a novel nomenclature of polycyclic aromatic hydrocarbons. Further, we derive some distinguishing theorems about PAH molecules and present some results of our automatic derivatization and automatic classification counting of fused PAH molecules.     

Asymptotically independent topological indices on random trees

Topological indices are graph invariants used in computational chemistry to encode molecules. A frequent problem when performing structure-activity studies is that topological indices are inter-correlated. We consider a simple topological index and show asymptotic independence for a random tree model. This continues previous work on the correlation among topological indices. These findings suggest that a size-dependence in a certain class of distance-based topological indices can be eliminated.AMS subject classification: 05C80, 60E10, 92E10     

Large cycles in random generalized Johnson graphs

This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.     

Two Hamiltonian cycles

If the line graph of a graph G decomposes into Hamiltonian cycles, what is G? We answer this question for decomposition into two cycles.     

Oriented hypergraphs: Balanceability

An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance.     

Hamilton cycles in line graphs of 3-hypergraphs

We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.     

On bandwidth sums of graphs

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CHAOS FOR MIXING TRANSFORMATIONS

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Two-Arc Transitive Graphs and Twisted Wreath Products

The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x ^–1 for all x F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given.     

Estimations of subgraph positions in molecular graphs and their common subgraph peculiarities

Some questions emerged from electronic data processing of molecular structures (graphs) and its fragments have been considered in this work. Quantitative estimations of subgraph positions in molecular graphs are presented and some properties of their maximal common subgraphs are described.