Khodakhast Bibak The number of spanning trees in an (r, s)-semiregular graph and its line graph International Journal of Quantum Chemistry 113
Graphs, among other things, may be thought of as representing the connectivity of the atoms that comprise the (microscopic) conjugation network of an unsaturated molecule. Calculating the number of spanning trees in (i.e., the complexity of) such (labeled) molecular graphs, and their remarkable applications have absorbed much attention. This article, after reviewing some of these applications, gives short proofs for complexities of a semiregular graph and its line graph. The green edges in the figure show a spanning tree.
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