Introduction to spectral graph theory
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چکیده
We write M ∈ Rn×n to denote that M is an n×n matrix with real elements, and v ∈ Rn to denote that v is a vector of length n. Vectors are usually taken to be column vectors unless otherwise specified. Recall that a real matrix M ∈ Rn×n represents a linear operator from Rn to Rn. In other words, given any vector v ∈ Rn, we think of M as a function which maps it to another vector w ∈ Rn, namely the matrix-vector product. Moreover, this function is linear: M(v1 + v2) = Mv1 + Mv2 for any two vectors v1 and v2, and M(λv) = λMv for any real number λ and any vector v. The perspective of matrices as linear operators is important to keep in mind throughout this course.
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SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
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