3 papers
math.CO2025
Graphs with given automorphism group and large clique number
John Haslegrave
Barbieri recently showed that the finite graphs realising any given finite automorphism group have unbounded genus, answering a question of Cornwell et al. In this note we give a s…
math.CO2024
The extremal generalised Randić index for a given degree range
John Haslegrave
O and Shi proved that the Randić index of any graph with minimum degree at least and maximum degree at most is at least , with equality if and…
math.CO2024
Lower bounds for the Randić index in terms of matching number
Saieed Akbari, Sina Ghasemi Nezhad, Reyhane Ghazizadeh +2
We investigate how small the Randić index of a graph can be in terms of its matching number, and prove several results. We give best-possible linear bounds for graphs of small exce…