{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852727,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>\r\n\r\n\r\nUsing 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.\r\n\r\n\r\n<\/jats:p>","DOI":"10.37236\/9785","type":"journal-article","created":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T01:48:47Z","timestamp":1702518527000},"source":"Crossref","is-referenced-by-count":0,"title":["Chromatic Polynomials of 2-Edge-Coloured Graphs"],"prefix":"10.37236","volume":"30","author":[{"given":"Iain","family":"Beaton","sequence":"first","affiliation":[]},{"given":"Danielle","family":"Cox","sequence":"additional","affiliation":[]},{"given":"Christopher","family":"Duffy","sequence":"additional","affiliation":[]},{"given":"Nicole","family":"Zolkavich","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,12,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T01:48:47Z","timestamp":1702518527000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i4p40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,15]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,10,6]]}},"URL":"https:\/\/doi.org\/10.37236\/9785","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,12,15]]},"article-number":"P4.40"}}