2024/08/23 by Manouchehr Zaker, Zaker, Manouchehr · 1 citation
Computer Science · #05C15 #05C85 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2408.12951
openalex publication_date 2024/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a simple graph and c a proper vertex coloring of G. A vertex u is called b-vertex in (G,c) if all colors except c(u) appear in the neighborhood of u. By a \rm b∗-coloring of G using colors \1, …, k\ we define a proper vertex coloring c such that there is a b-vertex u (called nice vertex) such that for each j∈ \1, …, k\ with j\not=c(u), u is adjacent to a b-vertex of color j. The \rm b∗-chromatic number of G (denoted by \rm b∗(G)) is the largest integer k such that G has a \rm b∗-coloring using k colors. Every graph G admits a \rm b∗-coloring which is an improvement over the famous b-coloring. A z-coloring of G is a coloring c using colors \1, 2, …, k\ containing a nice vertex of color k such that for each two colors i