Open AccessOn the irregular coloring of bipartite graph and tree graph families
Author(s) -
Q A’yun,
Dafik Dafik,
Robiatul Adawiyah,
Ika Hesti Agustin,
Ermita Rizki Albirri
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1836/1/012024
Subject(s) - combinatorics , bipartite graph , mathematics , brooks' theorem , edge coloring , complete coloring , greedy coloring , list coloring , discrete mathematics , graph coloring , fractional coloring , vertex (graph theory) , 1 planar graph , chordal graph , graph , graph power , line graph
This article discusses irregular coloring. Irregular coloring was first introduced by Mary Radcliffe and Ping Zhang in 2007. The coloring c is called irregular coloring if distinct vertices of G have distinct codes. The color code of a vertex v of G with respect to c is code(v) = (a 0 , a 1 , a 2 ,…, a k ) = a 0 a 1 a 2 , …a k , where a 0 = c(v) and a i , (1 < i < k) is the number of vertices that are adjacent to v and colored i. The minimum k-color used in irregular coloring is called the irregular chromatic number and is denoted by \ ir . Irregular coloring is included in proper coloring, where each vertex that is the neighbors must not be the same color. The graphs used in this article are a family of bipartite graphs and a family of tree graphs, including complete bipartite graphs, crown graphs, star graphs, centipede graphs, and double star graphs.