Abstract
Let G be a graph and let c:V(G)→{1,2…..k} be a coloring of the vertices of G for some positive integer k (where adjacent vertices may be colored the same). The color code of a vertex v of G (with respect to c) is the ordered (k+1)-tuple code (v) = (a0, a1, a2….ak) where a0 is the color assigned to v and for 1 ⩽ i ⩽ k, ai is the number of the vertices of G adjacent to that are colored i. The coloring c is called recognizable if distinct vertices have distinct color codes and the recognition number of G is the minimum positive integer k for which G has a recognizable k-coloring. In this paper we introduced a new variation of above parameter namely distance-2 irregular coloring. We initiate a study of this parameter and also find the distance 2-irregular chromatic number of some standard graphs.
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