Malaysian Journal of Mathematical Sciences, January 2015, Vol. 9, No. 1
Some Types of Spectral Distances between a Hypercube and its Complement and Line Graph
Mardjan Hakimi-Nezhaad and Ali-Reza Ashrafi
Corresponding Email: ashrafi@kashanu.ac.ir
Received date: -
Accepted date: -
Abstract:
Suppose $M_1$ and $M_2$ are two $n \times n$ matrices with eigenvalues $\lambda_{1}(M_{j}) \leq \lambda_{2}(M_{j}) \leq ... \leq \lambda_{n}(M_{j})$, $j = 1, 2$. The spectral distance between $M_1$ and $M_2$ is defined as $\sigma(M_{1}, M_{2})=\sum_{i=1}^{n}\left | \lambda_{i}(M_1) - \lambda_{i}(M_2) \right |$. In this paper , the Seidel, Laplacian , Signless Laplacian and Normalized Laplacian spectral distances of the hypercube and its complement , as well as the $k$ ? iterated line graphs of hypercube and its complements are computed . Some results on the spectral distance double cover are also presented.
Keywords: Seidel spectral distance , Laplacian spectral distance , Normalized Laplacian spectral distance, Signless Laplacian spectral distance , Extended double cover of graph.
Indexing
