Open AccessOn Locating Chromatic Number of Cubic Graph with Tree Cycle, Cn,2n,n, for n=3,4,5
Author(s) -
Salde Ofera,
Des Welyyanti,
Effendi
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 - 10.1088/1742-6596/1940/1/012020
Subject(s) - combinatorics , graph , vertex (graph theory) , partition (number theory) , chromatic scale , mathematics , physics , discrete mathematics
Let G = ( V ( G ), E ( G )) be a connected graph and is coloring of graph G . Let Π = { C 1 , C 2 , …, C k }, where C i is the partition of the vertex in which is colored i with 1 ≥ i ≥ k . The representation v for Π is called the color code, denoted C Π ( v ) is a ordered pair with k -element namely, C Π ( v ) = ( d ( v , C 1 ), d ( v , C 2 ), …, d ( v , C k )), where d ( v , C i )= mind{ d ( v , x )| xεC i } for 1 ≥ i ≥ k . If every vertex in G have different color code, the c is locating coloring. The minimum number of colors used in G is called chromatic locating, notated by X L ( G ). In this paper, we will determine the locating coloring of graph cubic C n,2n,n , for n=3,4,5.