This paper provides new upper bounds on the spectral radius \ (largest eigenvalue of the adjacency matrix) of graphs embeddable on a given compact surface. Our method is to bound the maximum rowsum in a polynomial of the adjacency matrix, using simple consequences of Euler's formula. Let # denote th
On the Spectral Radius and the Genus of Graphs
โ Scribed by H. Yuan
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 205 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0095-8956
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โฆ Synopsis
In this paper, we obtain a relation between the spectral radius and the genus of a graph. In particular, we give upper bounds on the spectral radius of graphs with (n) vertices and small genus. " " 1995 Academic Press. Ins
๐ SIMILAR VOLUMES
Let G be a simple graph with n vertices and orientable genus g and non-orientable genus h. Let \(G) be the spectral radius of the adjacency matrix A of G. We obtain the following sharp bounds of \(G): (1) \(G) 1+-3n+12g&8; (2) \(G) 1+-3n+6h&8.
We provide upper estimates on the spectral radius of a directed graph. In particular w e prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.