On encodings of spanning trees
نویسنده
چکیده
Deo and Micikevicius recently gave a new bijection for spanning trees of complete bipartite graphs. In this paper we devise a generalization of Deo and Micikevicius’s method, which is also a modification of Olah’s method for encoding the spanning trees of any complete multipartite graph K(n1, . . . , nr). We also give a bijection between the spanning trees of a planar graph and those of any of its planar duals. Finally we discuss the possibility of bijections for spanning trees of DeBriujn Graphs, Cubes, and regular graphs such as the Petersen graph that have integer eigenvalues. 2000 AMS Subject Classification: 05C05, 05C85, 68R10
منابع مشابه
Counting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملOn relation between the Kirchhoff index and number of spanning trees of graph
Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning tree...
متن کاملProviding a Simple Method for the Calculation of the Source and Target Reliabili- ty in a Communication Network (SAT)
The source and target reliability in SAT network is de- fined as the flawless transmission from the source node to all the other nodes. In some references, the SAT pro- cess has been followed between all the node pairs but it is very time-consuming in today’s widespread networks and involves many costs. In this article, a method has been proposed to compare the reliability in complex networks b...
متن کاملProviding a Simple Method for the Calculation of the Source and Target Reliabili- ty in a Communication Network (SAT)
The source and target reliability in SAT network is de- fined as the flawless transmission from the source node to all the other nodes. In some references, the SAT pro- cess has been followed between all the node pairs but it is very time-consuming in today’s widespread networks and involves many costs. In this article, a method has been proposed to compare the reliability in complex networks b...
متن کامل2 J ul 2 00 1 Orderly Spanning Trees with Applications ∗ Hsueh -
We introduce and study the orderly spanning trees of plane graphs. This algorithmic tool generalizes canonical orderings, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an orderly pair for any connected planar graph G, consisting of a plane graph H of G, and an orderly spanning tree of H. We also...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 155 شماره
صفحات -
تاریخ انتشار 2007