TOPICS
Search

Signless Laplacian Matrix

The signless Laplacian matrix of a graph G is

Q(G)=D(G)+A(G),

where D(G) is the degree matrix and A(G) is the adjacency matrix. It differs from the ordinary Laplacian matrix L=D-A only in the sign of the off-diagonal adjacency term.

The matrix Q is a positive semidefinite matrix. The multiplicity of its zero eigenvalue is the number of connected components of G that are bipartite graphs.

See also

Adjacency Matrix, Degree Matrix, Laplacian Matrix, Signless Laplacian Spectral Radius

Explore with Wolfram|Alpha

References

Cvetković, D.; Rowlinson, P.; and Simić, S. K. "Signless Laplacians of Finite Graphs." Linear Algebra Appl. 423, 155-171, 2007. https://doi.org/10.1016/j.laa.2007.01.009.Li, W.-J.; Wang, Z.; and Guo, J.-M. "The (Signless) Laplacian Spectral Radius with a Fixed Induced Subgraph of a Graph." Electron. J. Combin. 33, P3.81, 2026. https://doi.org/10.37236/12935.

Cite this as:

Weisstein, Eric W. "Signless Laplacian Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SignlessLaplacianMatrix.html

Subject classifications