๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the spectral radius of weighted trees with fixed diameter and weight set

โœ Scribed by Shang-wang Tan; Yan-hong Yao

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
222 KB
Volume
431
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

โœฆ Synopsis

The spectrum of weighted graphs are often used to solve the problems in the design of networks and electronic circuits. We first give some perturbational results on the spectral radius of weighted graphs when some weights of edges are modified, then we derive the weighted tree with the largest spectral radius in the set of all weighted trees with fixed diameter and weight set. Furthermore, an open problem of spectral radius on weighted paths is solved [H.Z. Yang, G.Z. Hu, Y. Hong, Bounds of spectral radii of weighted tree, Tsinghua Sci. Technol. 8 (2003) 517-520].

๐Ÿ“œ SIMILAR VOLUMES

On the spectral radius of trees with fix
On the spectral radius of trees with fixed diameter
โœ Ji-Ming Guo; Jia-Yu Shao ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 192 KB

Let T (n,d) be the set of trees on n vertices with diameter d. In this paper, the first d 2 + 1 spectral radii of trees in the set T (n,d) (3 d n -4) are characterized.

On the spectral radius of bipartite grap
On the spectral radius of bipartite graphs with given diameter
โœ Mingqing Zhai; Ruifang Liu; Jinlong Shu ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 123 KB

Let GB(n, d) be the set of bipartite graphs with order n and diam- eter d. This paper characterizes the extremal graph with the maximal spectral radius in GB(n, d). Furthermore, the maximal spectral radius is a decreasing function on d. At last, bipartite graphs with the second largest spectral radi