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October 2008 The Chromatic Polynomial of $P_2 \times P_n$ and $C_3 \times P_n$
Thomas J. Pfaff, Jasmine Walker
Missouri J. Math. Sci. 20(3): 169-177 (October 2008). DOI: 10.35834/mjms/1316032776


We provide formulas for the chromatic polynomials of the Cartesian product of a path on two vertices with a path on $n$ vertices, and a cycle on three vertices with a path on $n$ vertices. The result for the Cartesian product of paths involves the trinomial coefficients. We define a new sequence of numbers, $CP(n,i)$, which are part of the result for the chromatic polynomial of the Cartesian product of the three cycle and the path. In both cases the chromatic polynomial is factored in the form $\lambda (\lambda -1)$.


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Thomas J. Pfaff. Jasmine Walker. "The Chromatic Polynomial of $P_2 \times P_n$ and $C_3 \times P_n$." Missouri J. Math. Sci. 20 (3) 169 - 177, October 2008.


Published: October 2008
First available in Project Euclid: 14 September 2011

zbMATH: 1170.05026
Digital Object Identifier: 10.35834/mjms/1316032776

Primary: 05C15
Secondary: 05C38

Rights: Copyright © 2008 Central Missouri State University, Department of Mathematics and Computer Science


Vol.20 • No. 3 • October 2008
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