Open AccessOn r-dynamic local irregularity vertex coloring of special graphs
Author(s) -
I. N. Maylisa,
Dafik Dafik,
Alfian Futuhul Hadi,
Arika Indah Kristiana,
Ridho Alfarisi
Publication year - 2020
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 - 10.1088/1742-6596/1465/1/012013
Subject(s) - combinatorics , vertex (graph theory) , fractional coloring , complete coloring , mathematics , graph , edge coloring , circulant graph , list coloring , neighbourhood (mathematics) , discrete mathematics , graph power , line graph , mathematical analysis
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 { l i }; l i 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.