Webwe consider non-degenerate cyclic 7-edge-cuts and prove that there exist precisely two fullerenes with non-degenerate cyclic 7-edge-cut, which are not nanotubes. An important notion in this paper is a cut-vector. Let G be a fullerene graph and C a k-edge cut in G, and let H be one of the two components of the graph G −C.Let WebNov 23, 2012 · The structure of cyclic edge-cuts of fullerene graphs of sizes at most 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerate and non ...

A fullerene with a non-trivial cyclic 5-edge-cut. - ResearchGate

WebJul 1, 2008 · In this paper, we study cyclic edge-cuts in fullerene graphs. First, we show that the cyclic edge-cuts of a fullerene graph can be constructed from its trivial cyclic … WebIt is shown that every pair of hexagons in a fullerene graph satisfying the isolated pentagon rule (IPR) forms a resonant pattern. We show that every pair of hexagons in a fullerene graph satisfying the isolated pentagon rule (IPR) forms a resonant pattern. This solves a problem raised by Ye, Qi, and Zhang [SIAM J. Discrete Math., 23 (2009), pp. 1023-1044]. bam bryant

The isolated-pentagon rule and nice substructures …

WebSep 21, 2007 · In this paper, we study cyclic edge-cuts in fullerene graphs. First, we show that the cyclic edge-cuts of a fullerene graph can be constructed from its trivial cyclic … WebMar 17, 2007 · Formally, a graph G is cyclically k -edge connected if at least k edges must be deleted from G in order to separate it into two components such that both contain a … WebIn this paper, we study cyclic edge-cuts in fullerene graphs. First, we show that the cyclic edge-cuts of a fullerene graph can be constructed from its trivial cyclic 5- and 6-edge … bam brown alaskan bush people