On r-dynamic local irregularity vertex coloring of special graphs. (February 2020)

• Record Type: Journal Article
• Authors: Maylisa, I N; Dafik, ; Hadi, A F; Kristiana, A I; Alfarisi, R
• Is Part Of: Journal of physics. Volume 1465(2020)
• Publication Date: 2020-02
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1465/1/012013
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: In this paper, we study a new notion of graph coloring, that is a local irregularity vertex r -Dynamic coloring. We combine irregular local and the principles of r -dynamic coloring and we assign color to all vertices by using the weights of local irregularity vertex. We define l : V ( G ) → {1, 2, …, k } as a vertex irregular k -labeling and w : V ( G ) → N where w ( u ) = ∑ v ∈ N ( u ) l ( v ). By a local irregularity vertex coloring, we define a condition for f if for every uv ∈ E ( G ), w ( u ) ≠ w ( v ) and max ( l ) = min { max { li }; li vertex irregular labeling}. Each vertex of the weight as a color should satisfy the r -dynamic condition, namely | w ( N ( v )) ≥ min { r, d ( v )} and each the adjacent vertices must be different. In this paper, we study the local irregularity vertex r -Dynamic coloring of special graph, namely triangular book graph, central of friendship graph, tapol graph, and rectangular book graph.