New results on $B_α$-eigenvalues of a graph
By: Germain Pastén , Carla Silva Oliveira , João Domingos G. da Silva Junior and more
Potential Business Impact:
Finds patterns in connected things using math.
Let $G$ be a graph with adjacency matrix $A(G)$ and Laplacian matrix $L(G)$. In 2024, Samanta \textit{et} \textit{al.} defined the convex linear combination of $A(G)$ and $L(G)$ as $B_\alpha(G) = \alpha A(G) + (1-\alpha)L(G)$, for $\alpha \in [0,1]$. This paper presents some results on the eigenvalues of $B_{\alpha}(G)$ and their multiplicity when some sets of vertices satisfy certain conditions. Moreover, the positive semidefiniteness problem of $B_{\alpha}(G)$ is studied.
Similar Papers
On the distribution of $A_α$-eigenvalues in terms of graph invariants
Discrete Mathematics
Finds patterns in how things connect.
$k$-path graphs: experiments and conjectures about algebraic connectivity and $α$-index
Discrete Mathematics
Finds best ways to connect things in networks.
Distributed Sparsest Cut via Eigenvalue Estimation
Data Structures and Algorithms
Finds best ways to split computer networks.