A Study on Variants of Status Unequal Coloring in Graphs and Its Properties

Let G^ be a simple connected graph with vertex set ϑG^ and edge set ξG^. The status of a vertex p∈ϑG^ is defined as ∑q≠pdp,q. A subset P of ϑG^ is called a status unequal dominating set (stu-dominating set) of G^; for every q∈ϑ−P, there exists p in P such that p and q are adjacent and stp≠stq. Among the most admired, extensively explored, and extensively discussed topics in the field of graph theory is graph coloring. This article recommends a new research study on the topic of incorporating stu-dominating set with coloring. Diverse coloring variants can be found in literature, some of which serve as inspiration is chromatic number, dominator coloring, color class domination, and colorful dominating sets. A novel study on the topic of incorporating stu-dominating set with coloring is suggested in this article. The stu-chromatic number, stu-dominator coloring, stu-color class domination, and colorful stu-domination have thus been explored and investigated. For each parameter introduced, the minimum cardinality of certain standard classes of graphs, bounds, and characterization results was explored.