单圈图的邻和可区别边染色

Neighbor sum distinguishing edge coloring of unicyclic graphs

图G的一个k-正常边染色,若满足任意两个相邻点的色集合中所有元素之和不同,则称该染色为图G的一个k-邻和可区别边染色。其中,k的最小值称为图G的邻和可区别边色数。运用分析法与数学归纳法,研究了单圈图的邻和可区别边色数。

A proper k-edge coloring of graph G is a k-neighbor sum distinguishing edge coloring if the sum of all elements in the colors sets of any two adjacent vertices is different. The smallest value k is called the neighbor sum distinguishing edge chromatic number of G. The neighbor sum distinguishing edge chromatic numbers of unicyclic graphs are studied by the methods of analysis and mathematical induction.