#TITLE_ALTERNATIVE#

• Main Author: HELEN SIMARMATA (NIM : 90113015), RUTH
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/30732
• Institution: Institut Teknologi Bandung

<p align="justify">Closed modular chromatic number of &#119866; was introduced by Gary Chartrand, Futaba Okamoto, and Ping Zhang in 2010. For a nontrivial connected graph &#119866;, let &#119888;&#8758; &#119881; (&#119866;) &#8594; &#119885;&#119896; for a positive integer &#119896; be a vertex coloring where adjacent vertices may be assigned the same color. The coloring &#119888; induces another vertex coloring &#119888;&#8242;&#8758; &#119881; (&#119866;) &#8594; &#119885;&#119896; defined by &#119888;&#8242;(&#119907;)=&#931;&#119888;(&#119906;)&#119906;&#8712;&#119873;[&#119907;], for each &#119907; &#8712; &#119881; (&#119866;), where &#119873;[&#119907;] is the closed neighborhood of &#119907;. A coloring &#119888; is called a closed modular &#119896;-coloring if for every pair &#119909;,&#119910; of adjacent vertices in &#119866; either &#119888;&#8242;(&#119906;) &#8800; &#119888;&#8242;(&#119907;) or &#119873;[&#119909;] = &#119873;[&#119910;], in the latter case of which we must have &#119888;&#8242;(&#119909;)= &#119888;&#8242;(&#119910;). The minimum &#119896; for which &#119866; has a closed modular &#119896;-coloring is the closed modular chromatic number &#119898;&#119888;&#773;&#773;&#773;&#773;(&#119866;) of &#119866;. In this project, it is determined the closed modular chromatic number for some wheel-like graph. The closed modular chromatic number is investigated for some wheel-like graph which is cycle, wheel, Jahangir, helm, flower, sun, sunflower and dutch windmill.<p align="justify">