Strong Local Colorings of Coronas

In this paper, we study strong local colorings of some important families of coronas. A local coloring of a graph G of order at least 2 is a function c : V (G) rightarrow N such that for every set S subseteq V (G) with 2 ≤ |S| ≤ 3, there exists two distinct vertices u, v in S such that |c(u) − c(v)| ≥ ms, where ms is the size of the induced subgraph S . The value of a local coloring c is the maximum color it assigns to a vertex of G. The local chromatic number of G is the minimum value of ny local coloring of G and we denote it by Xl(G). A local coloring of G with value Xl(G) is called a minimum local coloring of G. If a minimum local coloring of G uses all the Xl(G) colors then it is called a strong local coloring of G. If every minimum local coloring of G uses all the Xl(G) colors then G is called strong local colorable and in this case, its local chromatic number is called strong local chromatic number and is denoted by Xsl(G). In this paper, we have considered some important families of coronas and determined the strong local chromatic number, if it exists; otherwise, we have proved that they are not strong local colorable but local colorable and determined their local chromatic number