Proper Magic Sigma Coloring of Specific Graphs - Panuvit Chuaephon; Kittikorn Nakprasit (Computer Science Journal of Moldova)
A coloring $φ: V(G)→ \{1,2,…,k \}$ is called a magic sigma coloring of $G$ if the sum of colors of all the vertices in the neighborhood of each vertex of $G$ is the same. A graph that admits such a coloring is said to be magic sigma colorable. The minimum number $k$ required in a magic sigma coloring of a graph $G$ is called the magic sigma chromatic number, denoted by $σ_{m}(G)$. These concepts have been extensively studied and motivate us to define a new type of coloring as follows.