{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:44Z","timestamp":1753893824244,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A labeling of a graph is a function from the vertex set of the graph to some finite set. \u00a0Certain dynamical systems (such as topological Markov shifts) can be defined by directed graphs. \u00a0In these instances, a labeling of the graph defines a continuous, shift-commuting factor of the dynamical system. \u00a0We find sufficient conditions on the labeling to imply classification results for the factor dynamical system. \u00a0We define the topological entropy of a (directed or undirected) graph and its labelings in a way that is analogous to the definition of topological entropy for a shift space in symbolic dynamics. \u00a0We show, for example, if $G$ is a perfect graph, all proper $\\chi(G)$-colorings of $G$ have the same entropy, where $\\chi(G)$ is the chromatic number of $G$.<\/jats:p>","DOI":"10.37236\/2213","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:56:32Z","timestamp":1578711392000},"source":"Crossref","is-referenced-by-count":0,"title":["Graph Labelings and Continuous Factors of Dynamical Systems"],"prefix":"10.37236","volume":"20","author":[{"given":"Stephen M.","family":"Shea","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p70\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p70\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:23:31Z","timestamp":1579260211000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p70"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2213","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,3,31]]},"article-number":"P70"}}