1. Chromatic Polynomials of Signed Book Graphs
- Author
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Sehrawat, Deepak and Bhattacharjya, Bikash
- Subjects
Numerical Analysis ,Mathematics::Combinatorics ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Theoretical Computer Science ,05C22, 05C15 - Abstract
For $m \geq 3$ and $n \geq 1$, 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., Substantial text overlap with arXiv:1812.08382
- Published
- 2022