The average number of spanning trees in sparse graphs with given degrees
نویسندگان
چکیده
We give an asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence d = (d1, . . . , dn), provided that the number of edges is at least n + 12d 4 max, where dmax is the maximum degree. A key part of our argument involves establishing a concentration result for a certain family of functions over random trees with given degrees, using Prüfer codes.
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 کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
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 کاملDesigning Sparse Reliable Pose-Graph SLAM: A Graph-Theoretic Approach
In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of spanning trees is an open problem in general. To tackle this problem, several new theoretical results are established in this paper, including the monotone log-su...
متن کاملMOD-CHAR: An Implementation of Char’s Spanning Tree Enumeration Algorithm and Its Complexity Analysis
Abstruct -An implementation, called MOD-CHAR, of Char’s spanning tree enumeration algorithm [3] is discussed. Two complexity analyses of MOD-CHAR are presented. It is shown that MOD-CHAR leads to better complexity results for Char’s algorithm than what could be obtained using the straightforward implementation implied in Char’s original presentation 131. The class of graphs for which MOD-CHAR a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 63 شماره
صفحات -
تاریخ انتشار 2017