Characteristic Polynomials and Spectra of Some Block Circulant Graphs

Abstract

A block matrix A=(A_ij ) _n×n is called a block circulant matrix, denoted by C(A ₁₁, A ₁₂, …, A _1n ) if A_ij =A _1,j−i+1 for all 1⩽i, j⩽n, where A_ij is a matrix and j−i+1 is taken modulo n. Especially when all A_ij are of order 1, A is called a circulant matrix. A digraph is called a (block) circulant digraph if its adjacency matrix is congruent to a (block) circulant matrix. In this article we will calculate the characteristic polynomials and spectra of several special block circulant graphs having some physical and chemical backgrounds.

Key Words:

• Block circulant graph
• Characteristic polynomial
• spectrum

Acknowledgments

This project supported by NSFC (No.11171279,11171134).