A new edge selection heuristic for computing the Tutte polynomial of an undirected graph

نویسنده

  • Michael B. Monagan
چکیده

We present a new edge selection heuristic and vertex ordering heuristic that together enable one to compute the Tutte polynomial of much larger sparse graphs than was previously doable. As a specific example, we are able to compute the Tutte polynomial of the truncated icosahedron graph using our Maple implementation in under 15 minutes on a single CPU. This compares with a recent result of Haggard, Pearce and Royle whose special purpose C++ software took one week on 150 computers.

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

On the tutte polynomial of benzenoid chains

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

متن کامل

Flow Polynomial of some Dendrimers

Suppose G is an nvertex and medge simple graph with edge set E(G). An integervalued function f: E(G) → Z is called a flow. Tutte was introduced the flow polynomial F(G, λ) as a polynomial in an indeterminate λ with integer coefficients by F(G,λ) In this paper the Flow polynomial of some dendrimers are computed.

متن کامل

Edge-Selection Heuristics for Computing Tutte Polynomials

The Tutte polynomial of a graph, also known as the partition function of the q-state Potts model, is a 2-variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial and flow polynomial as partial evaluations, and various numerical invariants, such as the number of ...

متن کامل

Computation of the Network Reliability

It is known that a certain case of the all-terminal network reliability can be computed via the Tutte polynomial which is an invariant in graph theory. Recently, we have proposed a new approach of computing the Tutte polynomial of a graph of moderate size [9]. In this paper, by using it we analyze computation method of the general all-terminal network reliability and two-terminal network reliab...

متن کامل

Tutte polynomials of wheels via generating functions

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

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:
  • CoRR

دوره abs/1209.5160  شماره 

صفحات  -

تاریخ انتشار 2011