weighted graphIn this article, we extend Moon's classic formula for counting spanning trees in complete graphs containing a fixed spanning forest to complete bipartite graphs. Let (X,Y) $(X,Y)$ be the bipartition of the complete bipartite graph Km,n ${K}_{m,n}$ with ∣X∣=m $| X...
We first prove a general result for $K_4$-minor-free graphs on the existence of spanning trees with a specified maximum degree for each vertex, given a condition on the number of components obtained when we delete a set of vertices. We provide examples for which this condition is best ...
本期专栏为 “谱图理论” 系列的第13期,将介绍耶鲁大学教授、两届哥德尔奖得主 Daniel A. Spielman 所著图书 《Spectral and Algebraic Graph Theory》 (电子版链接) 第十三章 Ch13: Random Spanning Trees 中…
3.6.2.3Trees in graph theory Now it is time to introduce a more complicated concept of graph theory, that oftrees. Atreeis any sequence of graph edges containing no cycles. In fact, a tree can relate to any combination of reactions. Aspanning tree, or maximum tree, is a sequence of gra...
stereochemistry A0210 Algebra, set theory, and graph theoryIt is emphasized by means of counter-examples that the theorem of Gutman, Mallion and Essam (1983, Molec. Phys., 50, 859), for computing the number of spanning trees in a labelled graph, is generally valid only for planar graph...
The number of spanning trees in self- similar graphs. Ann. Comb., 15(2):355-380, 2011.The number of spanning trees in self-similar graphs, preprint, 2008.E. Teufl and S. Wagner, The number of spanning trees in self-similar graphs, 2008....
Spanning trees in regular graphs, Vanderbilt University (1980-1981) Computer Science Tech. Rep. CS-81-01 10. B.D. McKay Subgraphs of random graphs with specified degrees paper presented at the Twelfth Southeastern Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, 1981, Congress...
As a by-product we derive a formula for the number of spanning trees in Kn1 □ Kn2 which turns out to be n1n1 -2 n2n2 - 2 (n1 + n2)n1 -1) n2- 1).doi:10.7151/dmgt.1698AZARIJADepartmentJERNEJDepartmentarXivDiscussiones Mathematicae: Graph Theory...
In certain fields of graph theory it is often useful to find a minimum spanning tree of a weighted graph. Other optimization problems on spanning trees have also been studied, including the maximum spanning tree, the minimum tree that spans at least k vertices, the minimum spanning tree with ...
A new proof that the number of spanning trees of K m,n is m n−1 n m−1 is presented. The proof is similar to Prüfer’s proof of...