Pewarnaan Sisi Ketakteraturan Lokal Refleksif pada Keluarga Graf Planar

Abstract

All graph in this paper is simple and connected graph where $V(G)$ is vertex set and $E(G)$ is edge set. Let function $f : V(G)\longrightarrow \{0, 2,..., 2k_v\}$ as vertex labeling and a function $f: E(G)\longrightarrow \{1, 2,..., k_e\}$ as edge labeling where $k=max\{2k_v,k_e\}$ for $k_v,k_e$ are natural number. The weight of edge $ u,v\in E(G) $ under $f$ is $w(u)=f(u)+ \Sigma_{uv \in V(G)} f(uv)$. 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 $\chi_{lrecs}(G).$ Furthermore, the minimum $k$ required such that $\chi_{lrecs}(G)=\chi(G)$ is called a local reflexive edge color strength, denoted by \emph{lrecs}$(G)$. In this paper, we learn about the local edge irregular reflexive coloring and obtain \emph{lrecs}$(G)$ of planar related graphs.