Titlebook: Irregularity in Graphs; Akbar Ali,Gary Chartrand,Ping Zhang Book 2021 The Author(s), under exclusive license to Springer Nature Switzerlan

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Royal Colorings,ph by assigning integers of the set [.] to the edges of the graph. For each vertex ., rather than adding or averaging the colors of the edges incident with ., they assigned the set of colors of the edges incident with ., with the goal of minimizing . so that distinct vertices have distinct subsets o

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Traversable Irregularity,ontains every edge of . at least once. While only Eulerian graphs contain an Eulerian circuit, every nontrivial connected graph contains an Eulerian walk. The irregularity concept here is an irregular Eulerian walk in ., which is an Eulerian walk where no two edges of . are encountered the same numb

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es. PcG proteins maintain silent states of gene expression, while the trxG of genes counteracts silencing with a chromatin opening function. These factors form multimeric complexes that act on their target chromatin by regulating post-translational modifications of histones as well as ATPdependent r

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Akbar Ali,Gary Chartrand,Ping Zhang, exposure to an environment that induces susceptibility to a disease may produce similar familial aggregations when the environment is shared by family members. In general, according to the principles of (Johannsen 1903), the emergence of a disease phenotype is the result of the combined effects of

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Akbar Ali,Gary Chartrand,Ping Zhangfactors on inheritance. Epigenetic states may contribute to the penetrance of genetic polymorphisms or mutations and thereby modify inheritance patterns. This may result in non‐Mendelian inheritance of genetic traits such as observed in common human disease. The relationship between epigenetics and

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Akbar Ali,Gary Chartrand,Ping Zhangfactors on inheritance. Epigenetic states may contribute to the penetrance of genetic polymorphisms or mutations and thereby modify inheritance patterns. This may result in non‐Mendelian inheritance of genetic traits such as observed in common human disease. The relationship between epigenetics and