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The second largest eigenvalue of a tree

โœ Scribed by A. Neumaier


Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
981 KB
Volume
46
Category
Article
ISSN
0024-3795

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๐Ÿ“œ SIMILAR VOLUMES


On the second largest eigenvalue of line
โœ Petrovi?, Miroslav; Mileki?, Bojana ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 169 KB ๐Ÿ‘ 2 views

In this paper all connected line graphs whose second largest eigenvalue does not exceed 1 are characterized. Besides, all minimal line graphs with second largest eigenvalue greater than 1 are determined.

The kth Laplacian eigenvalue of a tree
โœ Ji-Ming Guo ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 102 KB

## Abstract Let ฮป~__k__~(__G__) be the __k__th Laplacian eigenvalue of a graph __G__. It is shown that a tree __T__ with __n__ vertices has $\lambda\_{k}(T)\le \lceil { {n}\over{k}}\rceil$ and that equality holds if and only if __k__ < __n__, __k__|__n__ and __T__ is spanned by __k__ vertex disjoin

The largest induced tree in a sparse ran
โœ W. Fernandez de la Vega ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 192 KB ๐Ÿ‘ 2 views

The author proved that, for c > 1, the random graph G(n, p ) on n vertices with edge probability p = c / n contains almost always an induced tree on at least q n ( 1 -o( 1)) vertices, where L Y ~ is the positive root of the equation CLY = log( 1 + c'a). It is shown here that if c is sufficiently lar

On the second eigenvalue of a graph
โœ A. Nilli ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 241 KB

Nilli, A., On the second eigenvalue of a graph, Discrete Mathematics 91 (1991) 207-210. It is shown that the second largest eigenvalue of the adjacency matrix of any G containing two edges the distance between which is at least 2k + 2 is at least (2G -l)/(k + 1).

The largest tree in certain models of ra
โœ Ljuben Mutafchiev ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 227 KB ๐Ÿ‘ 2 views

We consider four families of forests on n vertices: labeled and unlabeled forests containing rooted and unrooted trees, respectively. A forest is chosen uniformly from one of the given four families. The limiting distribution of the size of its largest tree is then studied as n ยช ฯฑ. Convergences to