Explain why the spectrum of a graph is independent of vertex labeling.
What will be an ideal response?
When we change the vertex labeling, i.e., when we permute the vertex labels, the new adja-
cency matrix can be written in the form Anew = P?1AP, where P is a permutation matrix and
A is old adjacency matrix. Therefore, the new adjacency matrix is similar to the old one.
Hence, the eigenvalues of the matrix does not change.
Computer Science & Information Technology
You might also like to view...
When a slide is duplicated the slide layout, and content, is duplicated but not its formatting
Indicate whether the statement is true or false
Computer Science & Information Technology
If you want to resize several objects as a single object, you can ________ the individual objects
A) gather B) merge C) format D) group
Computer Science & Information Technology