8 papers
AVD Total Colorings of Subdivision Graphs, Joins, and Deleted Lexicographic Products
Amitayu Banerjee
In 2020, Panda, Verma, and Keerti asked whether the central graph of every graph satisfies the AVD-total coloring conjecture. In this paper, we verify the conjecture for central gr…
Automorphism groups and Distinguishing Colorings of Central and Middle Graphs
Amitayu Banerjee, Alexa Gopaulsingh, Zalán Molnár
Let G be a simple, finite, connected, and undirected graph. The middle graph M(G) of G is obtained from the subdivision graph S(G) after joining pairs of subdivided vertices that l…
Automorphism Groups and Structure of 4-Valent Cayley Graphs on Dihedral Groups
Amitayu Banerjee
Let be a finite group and let be an inverse-closed subset of not containing the identity. The Cayley graph has vertex set , where two vertices $x…
The List-distinguishing chromatic number of graphs containing only small complete bigraphs
Amitayu Banerjee
In 2006, Collins and Trenk obtained a general sharp upper bound for the distinguishing chromatic number of a connected graph. Inspired by Catlin's combinatorial techniques from 197…
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…
Brooks' type theorems for coloring parameters of locally finite graphs and Konig's Lemma
Amitayu Banerjee, Zalán Molnár, Alexa Gopaulsingh
In the past, analogues to Brooks' theorem have been found for various parameters of graph coloring for infinite locally finite connected graphs in ZFC. We prove these theorems are…