Pewarnaan Sisi Ketakteraturan Lokal Refleksif pada Keluarga Graf Planar - Nuwaila Izzatul Muttaqi; Dafik Dafik; Robiatul Adawiyah (jcgant, 2022)
All graph in this paper is simple and connected graph where V(G) is vertex set and E(G) is edge set. Let function f : V(G){0, 2,..., 2k_v} as vertex labeling and a function f: E(G){1, 2,..., k_e} as edge labeling where k=max{2k_v,k_e} for k_v,k_e are natural number. The weight of edge u,vE(G) under f is w(u)=f(u)+ Σ_uv V(G) f(uv). In other words, the function f is called local edge irregular reflexive labeling if every two adjacent edges has distinct weight and weight of a edge is defined as the sum of the labels of edge and the labels of all vertex incident this edge When we assign each edge of G with a color of the edge weight w(uv), thus we say the graph G admits a local edge irregular reflexive coloring. The minimum number of colors produced from local edge irregular reflexive coloring of graph G is reflexive local irregular chromatic number denoted by χ_lrecs(G). Furthermore, the minimum k required such that χ_lrecs(G)=χ(G) is called a local reflexive edge color strength, denoted by lrecs(G). In this paper, we learn about the local edge irregular reflexive coloring and obtain lrecs(G) of planar related graphs.