A formula for the number of spanning trees in circulant graphs with non-fixed generators∗

نویسنده

  • Justine Louis
چکیده

We consider the number of spanning trees in circulant graphs of βn vertices with generators depending linearly on n. The matrix tree theorem gives a closed formula of βn factors; while we derive a formula of β−1 factors. The spanning tree entropy of these graphs is then compared to the one of fixed generated circulant graphs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

NUMBER 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 کامل

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 کامل

N ov 2 01 7 The number of spanning trees in circulant graphs , its arithmetic properties and asymptotic

In this paper, we develop a new method to produce explicit formulas for the number τ(n) of spanning trees in the undirected circulant graphs Cn(s1, s2, . . . , sk) and C2n(s1, s2, . . . , sk, n). Also, we prove that in both cases the number of spanning trees can be represented in the form τ(n) = p n a(n), where a(n) is an integer sequence and p is a prescribed natural number depending only of p...

متن کامل

Counting Spanning Trees and Other Structures in Non-constant-jump Circulant Graphs

Circulant graphs are an extremely well-studied subclass of regular graphs, partially because they model many practical computer network topologies. It has long been known that the number of spanning trees in n-node circulant graphs with constant jumps satisfies a recurrence relation in n. For the non-constant-jump case, i.e., where some jump sizes can be functions of the graph size, only a few ...

متن کامل

Chebyshev polynomials and spanning tree formulas for circulant and related graphs

Kirchhoo's Matrix Tree Theorem permits the calculation of the number of spanning trees in any given graph G through the evaluation of the determinant of an associated matrix. In the case of some special graphs Boesch and Prodinger 9] have shown how to use properties of Chebyshev polyno-mials to evaluate the associated determinants and derive closed formulas for the number of spanning trees of g...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013