Alladi Ramakrishnan Hall

On distinguishing proper q-caterpillars by their chromatic symmetric functions

Sagar Sawant

IIT Madras

In 1995, Richard Stanley introduced a generalization of the chromatic polynomial of graphs to a symmetric function known as the chromatic symmetric function. While the chromatic polynomials of trees with the same order are identical, the chromatic symmetric functions of trees present a contrasting scenario. Stanley's Tree Isomorphism Conjecture posits that the chromatic symmetric function can distinguish non-isomorphic trees. This conjecture has already been established for caterpillars and other subclasses of trees. In this talk, we will discuss the validity of the conjecture for a new class of trees that generalize proper caterpillars, thereby confirming the conjecture for a broader class of trees.

This is joint work with G. Arunkumar, N. Narayanan, Raghvendra Rao B. V.