Distance-2 Irregular chromatic numbers for some graphs. Issue 1 (January 2021)

• Record Type: Journal Article
• Authors: Yokesh, D.; Nirmala, G.; Anitha, K.
• Is Part Of: Journal of physics. Volume 1724:Issue 1(2021)
• Publication Date: 2021-01
• Subjects: Irregular coloring -- chromatic number -- Path -- Cycle; Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1724/1/012026
• Languages: English
• ISSNs: 1742-6588

Abstract

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.