3 papers
math.CO2025
On Distinguishing Graphs and Cost Number using Automorphism Representations
Alexa Gopaulsingh, Zalán Molnár, Amitayu Banerjee
A distinguishing coloring of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A 2-distinguishable graph is a graph which c…
math.LO2025
Notes on ultrafilter extensions of almost bounded structures
Zalán Molnár
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one bin…
math.CO2024
Distinguishing chromatic number of middle and subdivision graphs
Amitayu Banerjee, Alexa Gopaulsingh, Zalán Molnár
Let be a simple finite connected graph of order greater than or equal to . We obtain the following results: (1). We apply a result of Hamada and Yoshimura from 1976 and…