Pewarnaan Titik Ketakteraturan Lokal Refleksif pada Keluarga Graf Tangga

Abstract

Let a simple and connected graph $G=(V,E)$ with the vertex set $V(G)$ and the edge set E(G). If there is a mapping $f$: $V(G)$ $\rightarrow$ ${0,2,…,2k_v}$ and $f$: $E(G)$ $\rightarrow$ ${1,2,…,k_e}$ as a function of vertex and edge irregularities labeling with $k=max$ ${2k_v,k_e}$ for $k_v$ and $k_e$ natural numbers and the associated weight of vertex $u,v \in V(G)$ under $f$ is $w(u)=f(u)+\sum_{u,v\in E(G)}f(uv)$. Then the function $f$ is called a local vertex irregular reflexive labeling if every adjacent vertices has distinct vertex weight. When each vertex of graph $G$ is colored with a vertex weight $w(u,v)$, then  graph $G$ is said to have a local vertex irregular reflexive coloring. Minimum number of vertex weight is needed to color the vertices in graf $G$ such that any adjacent vertices are not have the same color is called a local vertex irregular reflexive chromatic number, denoted by $\chi_{(lrvs)}(G)$. The minimum $k$ required such that $\chi_{(lrvs)}(G)=\chi(G)$ where $\chi(G)$ is chromatic number of proper coloring on G is called local reflexive vertex color strength, denoted by $lrvcs(G)$. In this paper, we will examine the local reflexive vertex color strength of local vertex irregular reflexive coloring on the family of ladder graph.