Some Spectral Properties of the B_α Matrix of a Graph

2026/07/28 by Garrett Kepler
#math.CO

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Abstract

Recently, Samanta et al. introduced a unifying perspective to common graph-associated matrices through the matrix B_α(G)=αA(G)+(1-α)L(G) where α∈ [0,1]. We resolve an open problem regarding the positive semi-definiteness of B_α and similar matrices. We also explore eigenvector properties of B_α through edge and vertex removal. As a consequence, we provide a basis for results on the common graph-associated matrices.

Citations

• New results on B_α-eigenvalues of a graph
• Unifying adjacency, Laplacian, and signless Laplacian theories
• Merging the A- and Q-spectral theories

Related

• Unifying adjacency, Laplacian, and signless Laplacian theories
• New results on B_α-eigenvalues of a graph
• Bounds on A_α-eigenvalues using graph invariants
• Generalization of some results concerning eigenvalues of a certain class\n of matrices and some applications
• On the Eigenvalues of Graphs with Mixed Algebraic Structure