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) → 0, 2, . . . , 2kv and f: E(G) → 1, 2, . . . , ke as a function of vertex and edge irregularities labeling with k = max 2kv, ke for kv and ke natural numbers and the associated weight of vertex u, v ∈ V (G) under f is w(u) = f(u) + P u,v∈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 χ(lrvs)(G). The minimum k required such that χ(lrvs)(G) = χ(G) where χ(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.