Signed Chromatic Polynomials of Signed Book Graphs

TL;DR

This paper investigates the signed chromatic polynomials of signed Book graphs, providing a recursive formula and classifying signatures up to switching isomorphisms, advancing understanding of graph coloring in signed graphs.

Contribution

It introduces a recursive formula for signed chromatic polynomials of signed Book graphs and classifies signatures up to switching isomorphisms.

Findings

Derived a recursive formula for signed chromatic polynomials.

Classified signatures on Book graphs up to switching isomorphisms.

Extended computational methods for signed graph colorings.

Abstract

In 2015, Matthias Beck and his team developed a computer program in SAGE which efficiently determines the number of signed proper $k$-colorings for a given signed graph. In this article, we determine the number of different signatures on Book graph up to switching isomorphisms. We also find a recursive formula of the signed chromatic polynomials of signed Book graphs.