The Complete b-chromatic sum of the Mycielskian of Paths

Source abstract

A b-coloring of a graph G is a proper vertex-coloring that for each class of color i, there is a vertex whose neighbors are of all colors but i. The b-chromatic number of G is the largest positive integer κ where a b-coloring of κ colors exists. The b-chromatic sum of G is the minimum sum of the colors of all vertices of G over all possible b-colorings that give the b-chromatic number. For the Mycielskian of path µ(Pn), the b-chromatic sum φ ′ (µ(Pn)) is known for all n except when 10 ≤ n ≤ 15. In this work, we give the value of φ ′ (µ(Pn)) when 10 ≤ n ≤ 15. This completes the list of the b-chromatic sum of µ(Pn).