2017/09/01 by Johan Kok, Sudev Naduvath, Kok, Johan +1 · 1 citation
Computer Science · Mathematics · #05C15 #05C38 #05C75 #05C85 #Advanced Graph Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1709.00261
openalex publication_date 2017/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a new invariant of a graph namely, the rainbow neighbourhood equate number of a graph G denoted by ren(G) is introduced. It is defined to be the minimum number of vertices whose removal results in a subgraph that admits a J-colouring. The new notions of chromatic degree of a vertex dχ(v), the maximum and minimum chromatic degrees of G denoted, Δχ(G) and δχ(G) respectively, are also introduced. The chromatic diameter of G denoted, d(G,χ) is introduced as well. The study of ren(G) appears to be very complex for graphs in general so for now, only introductory results will be presented. Finally, the concept of a chromatic degree sequence is proposed as a new research direction.