Pewarnaan Titik Ketakteraturan Lokal Refleksif pada Keluarga Graf Roda

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 vertex $ u,v\in V(G) $ under $f$ is $w(u)=f(u)+ \Sigma_{uv \in E(G)} f(uv)$. In other words, the function $f$ is called local vertex irregular reflexive labeling if every two adjacent vertices has distinct weight and weight of a vertex is defined as the sum of the labels of vertex and the labels of all edges incident this vertex When we assign each vertex of $G$ with a color of the vertex weight $w(uv)$, thus we say the graph G admits a local vertex irregular reflexive coloring. The minimum number of colors produced from local vertex irregular reflexive coloring of graph $G$ is reflexive local irregular chromatic number denoted by $\chi_{lrvs}(G).$ Furthermore, the minimum $k$ required such that $\chi_{lrvs}(G)=\chi(G)$ is called a local reflexive vertex color strength, denoted by \emph{lrvcs}$(G)$. In this paper, we learn about the local vertex irregular reflexive coloring and obtain \emph{lrvcs}$(G)$ of wheel related graphs.