Pewarnaan Sisi Ketakteraturan Lokal Refleksif pada Keluarga Graf Planar

Abstract

All graph in this paper are simple and connected graph. Let V (G) and E(G) be vertex 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 = max{2kv , 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 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 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.