The oriented chromatic number of edge-amalgamation of cycle graph

• Main Authors: Dina Eka Nurvazly, Jona Martinus Manulang, Kiki A. Sugeng
• Format: Article
• Language: English
• Published: InaCombS; Universitas Jember; dan Universitas Indonesia 2019-06-01
• Series: Indonesian Journal of Combinatorics
• Subjects: edge amalgamation of cycle; homomorphism; oriented chromatic number
• Online Access: http://www.ijc.or.id/index.php/ijc/article/view/61

<p>An oriented <span class="math"><em>k</em> − </span>coloring of an oriented graph <span class="math"><em>G⃗</em></span> is a partition of <span class="math"><em>V</em>(<em>G⃗</em>)</span> into <span class="math"><em>k</em></span> color classes such that no two adjacent vertices belong to the same color class, and all the arcs linking the two color classes have the same direction. The oriented chromatic number of an oriented graph <span class="math"><em>G⃗</em></span> is the minimum order of an oriented graph <span class="math"><em>H⃗</em></span> to which <span class="math"><em>G⃗</em></span> admits a homomorphism to <span class="math"><em>H⃗</em></span>. The oriented chromatic number of an undirected graph <span class="math"><em>G</em></span> is the maximum oriented chromatic number of all possible orientations of the graph <span class="math"><em>G</em></span>. In this paper, we show that every edge amalgamation of cycle graphs, which also known as a book graph, has oriented chromatic number less than or equal to six.</p>