Algebraic Connectivity and Degree Sequences of Trees (2008)
Biyikoglu, Türker; Leydold, Josef
We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are...
Graphs with given degree sequence and maximal spectral radius (2008)
Biyikoglu, Türker; Leydold, Josef
We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is...
Largest Eigenvalues of Degree Sequences (2006)
Biyikoglu, Türker; Leydold, Josef
We show that amongst all trees with a given degree sequence it is a ball where the vertex degrees decrease with increasing distance from its center that maximizes the spectral radius of the graph...
Largest Eigenvalues of Degree Sequences (2006)
Biyikoglu, Türker; Leydold, Josef
We show that amongst all trees with a given degree sequence it is a ball where the vertex degrees decrease with increasing distance from its center that maximizes the spectral radius of the graph...
Graph Laplacians, nodal domains, and hyperplane arrangements. (2004)
Pisanski, Tomaž, BIYIKOGLU, Türker, HORDIJK, Wim, LEYDOLD, Josef, STADLER, Peter
Eigenvectors of the Laplacian of a graph $G$ have received increasing attention in the recent past. Here we investigate their so-called nodal domains, i.e., the connected components of the maximal...
Faber-Krahn Type Inequalities for Trees (2003)
Biyikoglu, Türker; Leydold, Josef
The Faber-Krahn theorem states that among all bounded domains with the same volume in Rn (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been...
Faber-Krahn Type Inequalities for Trees (2003)
Biyikoglu, Türker; Leydold, Josef
The Faber-Krahn theorem states that among all bounded domains with the same volume in Rn (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been...
A Discrete Nodal Domain Theorem for Trees (2002)
Let G be a connected graph with n vertices and let x=(x1, ..., xn) be a real vector. A positive (negative) sign graph of the vector x is a maximal connected subgraph of G on vertices xi>0 (xi
A Discrete Nodal Domain Theorem for Trees (2002)
Let G be a connected graph with n vertices and let x=(x1, ..., xn) be a real vector. A positive (negative) sign graph of the vector x is a maximal connected subgraph of G on vertices xi>0 (xi