The Additive Coloring Problem is a variation of the Coloring Problem where labels of $\{1,\dots ,k\}$ are assigned to the vertices of a graph G so that the sum of labels over the neighborhood of each vertex is a proper coloring of G. The least value k for which G admits such labeling is called additive chromatic number of G. This problem was first presented by Czerwiński, Grytczuk and Żelazny who also proposed a conjecture that for every graph G, the additive chromatic number never exceeds the classic chromatic number. Up to date, the conjecture has been proved for complete graphs, trees, non-3-colorable planar graphs with girth at least 13 and non-bipartite planar graphs with girth at least 26. In this work, we show that the conjecture holds for split graphs. We also present exact formulas for computing the additive chromatic number for some subfamilies of split graphs (complete split, headless spiders and complete sun), regular bipartite, complete multipartite, fan, windmill, circuit, wheel, cycle sun and wheel sun.

加性着色问题是着色问题的变体，其中标签 $\{\mathrm{1个}，\dots ，ķ\}$分配给图G的顶点，以使每个顶点附近的标签和为G的正确着色。的最小值ķ为其ģ承认这样的标记被称为添加剂色数的ģ。这个问题最初由Czerwiński，Grytczuk和Żelazny提出，他们还提出了对每个图G的猜想。，加色数永远不会超过经典色数。迄今为止，已证明该猜想适用于完整图，树木，周长至少为13的非三色平面图和周长至少为26的非二分平面图。在这项工作中，我们证明了该猜想对分割图。我们还提供了精确的公式，用于计算某些分裂图子族（完全分裂，无头蜘蛛和完全太阳），规则二分，完全多部分，风扇，风车，电路，车轮，循环太阳和车轮太阳的加色数。