Some extremal problems for hereditary properties of graphs

TL;DR

This paper investigates extremal problems for hereditary graph properties, determining maximum edges and spectral radius in graphs of order n within these properties.

Contribution

It provides new bounds and results for extremal parameters like edges and spectral radius for graphs with hereditary properties.

Findings

Maximum number of edges in hereditary property graphs

Maximum spectral radius in hereditary property graphs

Extensions to other graph parameters

Abstract

This note answers extremal questions like: what is the maximum number of edges in a graph of order n, which belongs to some hereditary property. The same question is answered also for the spectral radius and other similar parameters.