Question: Let G be a disconnected simple graph. Prove that the chromatic polynomial P_G(k) of G is the product of the chromatic polynomials of the components

Let G be a disconnected simple graph. Prove that the chromatic

Let G be a disconnected simple graph. Prove that the chromatic polynomial P_G(k) of G is the product of the chromatic polynomials of the components of G. What can you say about the degree of the lowest non-vanishing term of P_G(k)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Chromatic Polynomial of Disconnected Graphs (a) (2 points) Prove that the chromatic polynomial of a disjoint graph is the the product of the polynomials of components. (b) (3 points) If G has r...

You$must$attach$this$cover$page$to$the$front$of$your$HW$or$you$will$lose$5$points.$ $ $ APMA$1860$Homework$2$ $ $ First$Name:$____________________________$$$Last$Name:$______________________________$...

answer all for practice la) What is the face chromatic number of the graph at the right? b) What is the edge chromatic number of the graph A G m at the right? B h 2. Find the chromatic polynomial for...

la) What is the face chromatic number of the graph at the right? b) What is the edge chromatic number of the graph at the right? 2. Find the chromatic polynomial for the graph on the right. P A B L b...

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

# 5: Fourier Interpolant and DFT 1 The Discrete Fourier Transform (DFT) of a periodic array fj , for j = 0, 1, . . . , N 1 (corresponding to data at equally spaced points, starting at the left end...

ANSI-SPARC6 Programming Language Compilation Write notes on each of the following topics: (a) the implementation of labels and jumps in a recursive, block structured programming language [7 marks]...

Assume that in preparing the cash budget, the accountant discovers that a cash shortage will likely occur in a specific month. What actions might the accountant recommend to management to deal with...

Gunnar & Dietar Consulting showed the following partners equity at August 31, 2014: Gunnar Schwiede, Capital................................................................................... $...

Present the following information in just one PowerPoint slide format with speaker key points. Our Plan of Reorganization would assume a calculated reorganization value of $245.23 million. Secured...

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

From a Comparable Worth Standpoint, what is the situation with regard to Federal Gender-based Employee Pay Equity?

Provide an example of how drilling down further into information can yield new results.

What do Dimensions represent in OLAP Cubes?