On eigenvalue multiplicity and the girth of a graph
β Scribed by P. Rowlinson
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 256 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
Let X be an infinite k-valent graph with polynomial growth of degree d, i.e. there is an integer d and a constant c such that fx(n) 3, d> 1, 123, there exist k-valent connected graphs with polynomial growth of degree d and girth greater than 1. This means that in general the girth of graphs with pol
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).
## a b s t r a c t For a connected graph G, the restricted edge-connectivity Ξ» β² (G) is defined as the minimum cardinality of an edge-cut over all edge-cuts S such that there are no isolated vertices in }, d(u) denoting the degree of a vertex u. The main result of this paper is that graphs with od