Geodesic
Chromatic polynomials of 2-edge-coloured graphs
Iain Beaton1 ; Danielle Cox2 ; Christopher Duffy3 ; Nicole Zolkavich4
1Department of Mathematics and Statistics, Dalhousie University
2Mathematics Department, Mount Saint Vincent University
3University of Melbourne
4Department of Mathematics and Statistics, McGill University
The electronic journal of combinatorics, Tome 30 (2023) no. 4
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Using the definition of colouring of $2$-edge-coloured graphs derived from 2-edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to 2-edge-coloured graphs. We find closed forms for the first three coefficients of this polynomial that generalize the known results for the chromatic polynomial of a graph. We classify those graphs that admit a 2-edge-colouring for which the chromatic polynomial of the graph and the chromatic polynomial of the 2-edge-colouring is equal. Finally, we examine the behaviour of the roots of this polynomial, highlighting behaviours not seen in chromatic polynomials of graphs.
DOI : 10.37236/9785
Classification : 05C15, 05C31
Mots-clés : signified graphs, homomorphisms of edge-coloured graphs

Iain Beaton  1   ; Danielle Cox  2   ; Christopher Duffy  3   ; Nicole Zolkavich  4

1 Department of Mathematics and Statistics, Dalhousie University
2 Mathematics Department, Mount Saint Vincent University
3 University of Melbourne
4 Department of Mathematics and Statistics, McGill University 
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Iain Beaton; Danielle Cox; Christopher Duffy; Nicole Zolkavich. Chromatic polynomials of 2-edge-coloured graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/9785

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