Randić, Milan; matematični kolokvij junij 2004

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Selected topics from chemical graph theory

Milan Randić

Drake University, ZDA

17. junij 2004

We will consider several topics from chemical graph theory that may benefit from involvement of mathematicians. First, we will outline some observations relating to the characteristic polynomial, isospectral graphs and subspectral graphs that may be of interest to be better explored by mathematicians. This will include Coulson's use of subgraph fragments for construction of characteristic polynomials, construction of isospectral graphs and some non-trivial properties of subspectral graphs.

The second topic relates to Kekule structures, Clar structures (a particular subset of Kekule structures), Resonance Graphs and the partition of pi-electrons to individual benzene rings. We end this section with exposure of Clar structures for non-benzenoid systems, including fullerenes.

The third topic to be discussed concerns "compact representation" of lengthy DNA sequences and proteins with outline of representation of sequences as maps, including a brief outline of the very recent representation of DNA sequences as "four color maps".

Finally, the last topic to be reviewed concerns the apparently "random" proteome maps (which are not random as will be demonstrated) and the somewhat unusual and unexpected properties of the "neighborhood" graphs that have yet to be mathematically better understood.

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