Normalized Laplacian spectrum of some subdivision-joins and -joins of two regular graphs

Abstract

In this paper we determine the full normalized Laplacian spectrum of the subdivision-vertex join, subdivision-edge join, -vertex join, and -edge join of two regular graphs in terms of the normalized Laplacian eigenvalues of the graphs. Moreover, applying these results we find non-regular normalized Laplacian cospectral graphs.

Keywords

• normalized laplacian matrix
• subdivision-vertex join
• subdivision-edge join
• -vertex join
• -edge join