Spektrum Laplace pada graf kincir angin berarah (Q_k^3)

Abstract

Suppose that 0 = µ₀ ≤ µ₁ ≤ ... ≤ µ_n-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ₀), m(µ₁), …, m(µ_n-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements are µ₀, µ₁, …, µ_n-1 for the first row, and m(µ₀), m(µ₁), …, m(µ_n-1) for the second row. In this paper, we will discuss Laplacian spectrum of the directed windmill graph () with k ≥ 1. The determination of the Laplacian spectrum in this study is to determine the characteristic polynomial of the Laplacian matrix from the directed windmill graph () with k ≥ 1.

Keywords: Characteristic polynomial, directed windmill graph, Laplacian matrix, Laplacian spectrum.
MSC2020 :05C50