Resolving Dominating Set pada Graf Bunga dan Graf Roda - Nabilah Ayu Az-Zahra; Dafik Dafik; R M Prihandini (jcgant, 2023)
All graphs in this paper are simple and connected graph. Let V (G) and E(G) bevertex set and edge set. A map f : .V (G) −→ 0, 2, ..., 2kv and f : E(G) −→ 1, 2, ..., ke are sind to be an irregular reflexive labelling where k = max2kv, ke for kv, ke are natural number. The weight of edge u, v ∈ E(G) under f is w(u) = f(u)+Σuv∈V (G)f(uv). 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 edgeWhen 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 χlrecs(G). Furthermore, the minimum k required such that χlrecs(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.