11 - 13 of 13 Chapters
[In the previous chapters, we have been considering vertex colourings. Now we will look at edge colourings of a graph. We will say that two edges are adjacent if they have a common vertex. We would like to colour the edges “properly” in the sense that no two adjacent edges receive the same...
[Recall that a k-regular graph is one in which every vertex has degree k. Thus, every row sum (and hence every column sum) of its adjacency matrix A is k. We have seen (see Exercise 4.5.1) that k is an eigenvalue of A. Moreover, it is easy to see that all the eigenvalues λ satisfy |λ| ≤ k....
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