Bruce is right, it is not at all clear what do you need. Please give details and example. Also take a look at this MathWorld article. There is a link to an attached Mathematica notebook with code right below the tittle of the page.

Dear Reinaldo, please take a few minutes to learn how to make proper posts with this tutorial:

How to type up a post: editor tutorial & general tips

- especially posting code. You can see other people on the thread use proper tools for posting code. It seems that because you pasted code as plain text some parts of it are missing.

Example where does not work
In this example does not work the Chromatic Polynomial

Hi Reinaldo:

Did you look at the function ChromaticPolynomial ? it is from the Combinatorica package.

This uses the old Graph specification, all from the combinatorica package:

You probably have to use FromAdjacencyMatrix, and related functions from:
Combinatorica/guide/GraphConstructionAndRepresentations
^^ Look that up in the help.

Dear Vitaly Kaurov,
I have been working on graphs up to 16 vertices and the program to compute  works fine (it takes about  5 hours on my  Sony Laptop), however when I try a graph with 18 vertices does not work, ever after 26 hours (I aborted de computations). For intance, the following graph :

g= {{0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0,
  0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
  0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0,
  0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1}, {0,
  1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0,
  0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
  0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
  1}, {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 0,
  0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0,
  1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
  1, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0}};

Another question, the comand Constraction 
Contract[g,{x,y}]
is not working for us, or I do not how to used it.

g = {{0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 1, 0, 0,
     0, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1}, {0, 0, 1, 0, 1,
    0, 0, 0, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0}, {1, 0,
     0, 0, 0, 0, 0, 1, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0,
    0}, {0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0,
     0, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 0,
    0, 1, 0, 0, 1, 0, 0, 1}, {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0}};

 FromAdjacencyMatrix // ShowLabeledGraph


The graph is shown but the contract graph no
Contract[g, {1, 2}]

Thanks a lot in advance,
Your sincerely

Reinaldo Giudici

Another question, the command  Contract[g,{x,y}]i  s not working for us, or I do not how to used it.The graph is shown but the contract graph Contract[h, {1, 2}]
We tried to enter the matrix for the suggested method, but had no luck.
Thanks a lot in advance,Your sincerely
Reinaldo Giudici

you need to convert h to combinatorica graph like you did for chromatic polynomial:

Dear Reinaldo,

Chromatic polynomials are typically calculated using a deletion-contraction recursion, which is a very lengthy and awkward procedure to perform. The problem of computing such polynomials (which are a specialization of the Tutte polynomial) is $\#P$-hard in general, so one can not expect miracles of the "d-c" recursion, which I assume is the built-in method of Combinatorica.

Determinining whether a graph admits a $k$-coloring is known to be $NP$-complete for $k\geq 3$, but there exist various approximation algorithms for performing graph colorings that are somewhat optimal. In [1], Bonnie Berger and John Rompel developed an algorithm with a performance guarantee of $O(n(log~log~n)^3/(log~n)^3)$ and Magnús Halldórsson improved this result to $O(n(log~log~n)^2/(log~n)^3)$ in [2].

In 2009, a research group from New Zealand calculated the Tutte polynomial of the truncated icosahedron and, as their website explains, this took about one week to compute in a cluster of 150 computers [3]. So yes, computing the chromatic polynomial (more generally Tutte polynomial) of large graphs can be a complete nightmare as you already experienced. This is probably why finding efficient coloring algorithms remains one of the most exciting open challenges in combinatorics and computer science.

I hope this helps!

References:

[1] B. Berger and J. Rompel. A better performance guarantee for approximate graph coloring. Algorithmica, 1988.

[2] M. M. Halldórsson. A still better performance guarantee for approximate graph coloring. Information Processing Letters, 1993.

[3] "Code for Computing Tutte Polynomials" (http://homepages.ecs.vuw.ac.nz/~djp/tutte/)