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- Title
On the local irregularity vertex coloring of volcano, broom, parachute, double broom and complete multipartite graphs.
- Authors
Kristiana, Arika Indah; Nikmah, Nafidatun; Dafik; Alfarisi, Ridho; Hasan, M. Ali; Slamin
- Abstract
Let G = (V , E) be a simple, finite, undirected, and connected graph with vertex set V (G) and edge set E (G). A bijection l : V (G) → { 1 , 2 , ... , k } is label function l if opt (l) = min { max (l i) : l i v e r t e x i r r e g u l a r l a b e l i n g } and for any two adjacent vertices u and v , w (u) ≠ w (v) where w (u) = ∑ v ∈ N (u) l (v) and N (u) is set of vertices adjacent to v. w is called local irregularity vertex coloring. The minimum cardinality of local irregularity vertex coloring of G is called chromatic number local irregular denoted by χ l i s (G). In this paper, we verify the exact values of volcano, broom, parachute, double broom and complete multipartite graphs.
- Subjects
BROOMS &; brushes; COMPLETE graphs; GRAPH connectivity; GRAPH coloring; PARACHUTING; PARACHUTES; BIJECTIONS
- Publication
Discrete Mathematics, Algorithms & Applications, 2022, Vol 14, Issue 6, p1
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S1793830922500227