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Corpus ID: 119662278

Signed Chromatic Polynomials of Signed Book Graphs

@article{Deepak2018SignedCP,
title={Signed Chromatic Polynomials of Signed Book Graphs},
author={Deepak and Bikash Bhattacharjya},
journal={arXiv: Combinatorics},
year={2018}
}

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.

This paper proves that the maximum frustration of generalized Petersen graphs $P_{n,k}$ is bounded above by $\left\lfloor \frac{n}{2} \right\rfloor + 1$ for $\gcd( n,k)=1$ and this bound is achieved for $k=1,2,3$.Expand

We extend the work of Hanlon on the chromatic polynomial of an unlabeled graph to define the unlabeled chromatic polynomial of an unlabeled signed graph. Explicit formulas are presented for labeled… Expand

Zaslavsky proved in 2012 that, up to switching isomorphism, there are six different signed Petersen graphs and that they could be told apart by their chromatic polynomials, by showing that the latter… Expand

This paper is the first general study of signed graph homomorphisms, and reformulating Hadwiger's conjecture in the language of homomorphism of signed graphs whose underlying graph is bipartite shows that while some stronger form of the conjecture holds for small chromatic number, such strengthening of the conjectures would not hold for large chromatic numbers.Expand