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In this study, we propose a novel method for creating nutritious menus using vertex coloring, a fundamental concept in graph theory. Our team has combined the Welch-Powell algorithm with a mathematical combination technique to generate a range of menus that adhere to low-calorie nutritional guidelines while offering diversity. To showcase the practicality and efficacy of our approach, we have utilized dynamic simulation in Matlab, which generates three distinct diet combinations customized to meet specific nutritional needs. Our methodology can serve as a blueprint for developing balanced meal plans and underscores the flexibility of graph theory in real-world applications. Additionally, we have explored an alternative approach to arranging menus that employ vertex-disjoint paths in a graph, resulting in a streamlined process for creating diverse and nutritionally balanced menus. This study highlights the significance of innovative solutions for addressing the complexities of diet planning and provides valuable insights for future research. [ABSTRACT FROM AUTHOR]

MERS-CoV or generally called as Middle East Respiratory Syndrome Coronavirus, a respiratory disease syndrome caused by a corona virus that attacks the respiratory tract ranging from mild to severe acute indication of fever, cough and shortness of breath. The cases happened relate to the countries in the Arabian Peninsula (Middle East) and there were 356 deaths have been reported due to the spread of the epidemic MERS.The data used in the case of MERS are the data DNA sequences taken from Genbank, the online database of the United States that stores the results of molecular biological experiments from all over the world (http://www.ncbi.nlm.nih.gov). In this case, bioinformatics plays an important role of reading sequences of DNA and genetic information by using the main device in the form of software that is supported by the availability of the Internet, while the analysis there in made and proven with mathematical methods.In similar research conducted by molecular biologists and physicians, the process of DNA sequencing is done with software that is already available like BLAST. In order to determine the MERS geographical distribution patterns in the Arabian Peninsula is done with program Clustal W, Bayesian, Phylip, etc. In this study, the writer use the Matlab simulation for all processes starting sequence alignment, counting the number of transitions and transversion substitutions for each sequence and its location up to the process of forming a phylogenetic tree that figures out the pattern of spread of the epidemic MERS. Mathematical analysis performed on a decline in the formula is to find Kimura evolutionary models and the process of forming a phylogenetic tree (the pattern of the epidemic MERS distribution) with neighbor joining algorithm.Finally it was obtained the pattern of geographical spread with 6 groups epidemic of MERS which ultimately turns out that all the MERS viruses that were spread in the Arabian Peninsula everything are almost the same as the virus sequence found in al-Hasa. [ABSTRACT FROM AUTHOR]