#TITLE_ALTERNATIVE#
<p align="justify">Closed modular chromatic number of 𝐺 was introduced by Gary Chartrand, Futaba Okamoto, and Ping Zhang in 2010. For a nontrivial connected graph 𝐺, let 𝑐∶ 𝑉 (𝐺) → 𝑍Ү...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/30732 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | <p align="justify">Closed modular chromatic number of 𝐺 was introduced by Gary Chartrand, Futaba Okamoto, and Ping Zhang in 2010. For a nontrivial connected graph 𝐺, let 𝑐∶ 𝑉 (𝐺) → 𝑍𝑘 for a positive integer 𝑘 be a vertex coloring where adjacent vertices may be assigned the same color. The coloring 𝑐 induces another vertex coloring 𝑐′∶ 𝑉 (𝐺) → 𝑍𝑘 defined by 𝑐′(𝑣)=Σ𝑐(𝑢)𝑢∈𝑁[𝑣], for each 𝑣 ∈ 𝑉 (𝐺), where 𝑁[𝑣] is the closed neighborhood of 𝑣. A coloring 𝑐 is called a closed modular 𝑘-coloring if for every pair 𝑥,𝑦 of adjacent vertices in 𝐺 either 𝑐′(𝑢) ≠ 𝑐′(𝑣) or 𝑁[𝑥] = 𝑁[𝑦], in the latter case of which we must have 𝑐′(𝑥)= 𝑐′(𝑦). The minimum 𝑘 for which 𝐺 has a closed modular 𝑘-coloring is the closed modular chromatic number 𝑚𝑐̅̅̅̅(𝐺) of 𝐺. 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"> |
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