𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the second eigenvalue of a graph

✍ Scribed by A. Nilli


Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
241 KB
Volume
91
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


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).


πŸ“œ SIMILAR VOLUMES


On the second largest eigenvalue of line
✍ Petrovi?, Miroslav; Mileki?, Bojana πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 169 KB πŸ‘ 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.

Graphs characterized by the second eigen
✍ Dasong Cao; Hong Yuan πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 266 KB

## Abstract In this paper we prove that for a simple graph __G__ without isolated vertices 0 < Ξ»~2~(__G__) < 1/3 if and only if __G__ β‰… KΜ„~__n__‐3~ V (__K__~1~ βˆͺ __K__~2~), the graph obtained by joining each vertex of KΜ„~__n__‐3~ to each vertex of __K__~1~ βˆͺ __K__~2~). Β© 1993 John Wiley & Sons, Inc

A characterization of the smallest eigen
✍ Madhav Desai; Vasant Rao πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 549 KB

## Abstract It is well known that the smallest eigenvalue of the adjacency matrix of a connected __d__‐regular graph is at least βˆ’ __d__ and is strictly greater than βˆ’ __d__ if the graph is not bipartite. More generally, for any connected graph __G = (V, E)__, consider the matrix __Q = D + A__ wher

On the embedding of graphs into graphs w
✍ Vu, Van H. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 726 KB

A graph is called of type k if it is connected, regular, and has k distinct eigenvalues. For example graphs of type 2 are the complete graphs, while those of type 3 are the strongly regular graphs. We prove that for any positive integer n, every graph can be embedded in n cospectral, non-isomorphic