Chromatic Polynomials of Signed Book Graphs

Authors

Deepak Sehrawat, Indian Institute of Technology GuwahatiFollow
Bikash Bhattacharjya, Indian Institute of Technology - GuwahatiFollow

Abstract

For m ≥ 3 and n ≥ 1, the m-cycle book graph B(m,n) consists of n copies of the cycle C_m with one common edge. In this paper, we prove that (a) the number of switching non-isomorphic signed B(m,n) is n+1, and (b) the chromatic number of a signed B(m,n) is either 2 or 3. We also obtain explicit formulas for the chromatic polynomials and the zero-free chromatic polynomials of switching non-isomorphic signed book graphs.

Creative Commons License

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Recommended Citation

Sehrawat, Deepak and Bhattacharjya, Bikash (2022) "Chromatic Polynomials of Signed Book Graphs," Theory and Applications of Graphs: Vol. 9: Iss. 1, Article 4.
DOI: 10.20429/tag.2022.090104
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/4