| author: | Stavros D. Nikolopoulos and Charis Papadopoulos |
|---|---|
| title: | On the number of spanning trees of K graphsn m ± G |
| keywords: | Kirchhoff matrix tree theorem, complement spanning tree matrix, spanning trees, Kn-complements, multigraphs. |
| abstract: | The K -complement of a graph n G , denoted by K , is defined as
the graph obtained from the complete graph n -GK
by removing a set of edges that span n G ; if
G has n vertices, then K coincides with the
complement n -GG G . In this paper we
extend the previous notion and derive determinant based formulas
for the number of spanning trees of graphs of the form K , where n m
±GK is the complete multigraph on n m n vertices
with exactly m edges joining every pair of vertices and G is a
multigraph spanned by a set of edges of K ; the graph
n m K (resp. n m + GK ) is obtained from n m - GK by
adding (resp. removing) the edges of n m G . Moreover, we derive
determinant based formulas for graphs that result from K
by adding and removing edges of multigraphs spanned by sets of
edges of the graph n m K . We also prove closed formulas for the
number of spanning tree of graphs of the form n m K ,
where n m ± GG is (i) a complete multipartite graph, and (ii) a
multi-star graph. Our results generalize previous results and
extend the family of graphs admitting formulas for the number of
their spanning trees. |
| If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |
| reference: | Stavros D. Nikolopoulos and Charis Papadopoulos (2006),
On the number of spanning trees of K graphs,
Discrete Mathematics and Theoretical Computer Science 8, pp. 235-248n m ± G |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dm080114.ps.gz (161 K) |
| ps-source: | dm080114.ps (442 K) |
| pdf-source: | dm080114.pdf (143 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.