A recently discovered approach including de Brujin graphs and Eulerian circuits are used to DNA sequencing and fragment assembly, and to simplify DNA graphs through a series of transformations on graphs and digraphs i...A recently discovered approach including de Brujin graphs and Eulerian circuits are used to DNA sequencing and fragment assembly, and to simplify DNA graphs through a series of transformations on graphs and digraphs in the field of bioinformatics. Since numbered graphs provide underlying mathematical models in studying the wide variety of seemingly unrelated practical applications, so graph colorings often are used to divide large systems into subsystems. A new graph labeling has been introduced and investigated.展开更多
A proper total-coloring of graph G is said to be?equitable if the number of elements (vertices and edges) in any?two color classes differ by at most one, which the required?minimum number of colors is called the equit...A proper total-coloring of graph G is said to be?equitable if the number of elements (vertices and edges) in any?two color classes differ by at most one, which the required?minimum number of colors is called the equitable total chromatic?number. In this paper, we prove some theorems on equitable?total coloring and derive the equitable total chromatic numbers?of Pm V?Sn, Pm V?Fn and Pm V Wn.展开更多
文摘A recently discovered approach including de Brujin graphs and Eulerian circuits are used to DNA sequencing and fragment assembly, and to simplify DNA graphs through a series of transformations on graphs and digraphs in the field of bioinformatics. Since numbered graphs provide underlying mathematical models in studying the wide variety of seemingly unrelated practical applications, so graph colorings often are used to divide large systems into subsystems. A new graph labeling has been introduced and investigated.
文摘A proper total-coloring of graph G is said to be?equitable if the number of elements (vertices and edges) in any?two color classes differ by at most one, which the required?minimum number of colors is called the equitable total chromatic?number. In this paper, we prove some theorems on equitable?total coloring and derive the equitable total chromatic numbers?of Pm V?Sn, Pm V?Fn and Pm V Wn.
