A sharpened condition for strict log-convexity of the spectral radius via the bipartite graph

A Sharpened Condition for Strict Log-Convexity of the Spectral Radius via the Bipartite Graph

Friedland (1981) showed that for a nonnegative square matrix A, the spectral radius r(eA) is a log-convex functional over the real diagonal matrices D. He showed that for fully indecomposable A, log r(eA) is strictly convex over D1,D2 if and only if D1 −D2 6= c I for any c ∈ R. Here the condition of full indecomposability is shown to be replaceable by the weaker condition that A and A>A be irre...

Convexity and Log Convexity for the Spectral Radius

The starting point of this paper is a theorem by J. F. C. Kingman which asserts that if the entries of a nonnegative matrix are log convex functions of a variable then so is the spectral radius of the matrix. A related result of J. Cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements. The first section of this paper gives a new, unified pr...

Spectral radius of bipartite graphs

The Spectral Radius of A Planar Graph

A decomposition result for planar graphs is used to prove that the spectral radius of a planar graph on n vertices is less than 4 + 3(n 3) Moreover, the spectral radius of an outerplanar graph on n vertices is less than 1 + JZ+&-X

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...