roles) || in_array('administrator', $user->roles) || in_array('admin',$user->roles ) ) { ?>
probname); ?>
Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>
Topics: nid, "Topics"); ?> Prerequisites: nid, "Prerequisites"); ?>
Supplies: nid, "Supplies"); ?> Pedagogy: nid, "Pedagogy"); ?>

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Solution: nid, "Solution"); ?>
Problem

Given a graph $G$ and a positive integer $k$, let $c_G(k)$ be the number of colorings of $G$ that use at most $k$ colors.
Compute $c_G(k)$ for the following four classes:

The $\textit{null graph}$ $N_n$ consists of $n$ nodes and no edges.

The $\textit{complete graph}$ $K_n$ consists of $n$ nodes with all possible edges between them.

The $\textit{line graph}$ $L_n$ consists of $n$ nodes with edges that form a line segment.

The $\textit{cycle}$ $C_n$ consists of $n$ nodes with edges that form a circle.

What do you notice about

1. the leading coefficients?

2. the second leading coefficients?

3. the constant term?

4. the highest degree?

Details
Authors
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References
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Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
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DEFINITIONS
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