Year: 2024
Type: article
Abstract: An internal or friendly partition of a vertex set of a graph is a partition to two nonempty sets such that every vertex has at least as many neighbours in its own class as in the other one. Motivated by Diwan's existence proof on internal partitions of graphs with high girth, we give constructive proofs for the existence of internal partitions in the incidence graph of projective planes and discuss its geometric properties. In addition, we determine exactly the maximum possible difference between the sizes of the neighbour set in its own class and the neighbour set of the other class that can be attained for all vertices at the same time for the incidence graphs of Desarguesian planes of square order.
Source: Journal of Combinatorial Designs
DOI: 10.1002/jcd.21956
Author: Zoltán Lóránt Nagy
Institution: Eötvös Loránd University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G5214083379, G6997194206
OpenAlex ID: W4403170818