Chromatic Polynomials of Signed Book Graphs

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.