𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Some graphs with small second eigenvalue

✍ Scribed by Joel Friedman


Publisher
Springer-Verlag
Year
1995
Tongue
English
Weight
577 KB
Volume
15
Category
Article
ISSN
0209-9683

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Bipartite graphs with small third Laplac
✍ Xiao-Dong Zhang πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 420 KB

In this paper, all connected bipartite graphs are characterized whose third largest Laplacian eigenvalue is less than three. Moreover, the result is used to characterize all connected bipartite graphs with exactly two Laplacian eigenvalues not less than three, and all connected line graphs of bipart

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

On the second eigenvalue of a graph
✍ A. Nilli πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 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).

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.

Some Minimal Graphs by Interlacing Eigen
✍ H.B. Walikar; P.R. Hamipholi; H.S. Ramane πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 159 KB

Let \(G\) be a simple graph with \(p\) vertices and let \(A(G)\) be the adjacency matrix of \(G\). The characteristic polynomial of \(G\) is the characteristic polynomial of \(A(G)\) and roots of the characteristic equation are the eigenvalues of \(G\). In this paper we compute the characteristic po