On the Surface Area of Graphs, Related Connectivity Measures and Spectral Estimates
Abstract
Abstract In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a special class of large graphs, called social graphs, that might prove interesting for applications. In addition, we derive spectral estimates involving the surface area and, as a main result, present an upper bound on the second eigenvalue for planar graphs which in some cases improves upon existing bounds from [31] and [28].
Fields of Study & Subjects
Advanced Graph Theory Research
Interconnection Networks and Systems
Graph Theory and Algorithms
Publication details
- Journal / source
- Complex Analysis and Operator Theory
- Publisher
- Springer Science and Business Media LLC
- Volume
- 20
- Issue
- 3
- Publication date
- 6 March 2026
- Language
- EN