Pewarnaan Sisi r-Dinamis pada Graf Khusus dan Graf Operasi Sakel

Abstract

Let G = (V (G), E(G)) be a nontrivial connected graph. The edge coloring is defined as c : E(G) → {1, 2, ..., k}, k ∈ N, with the condition that no adjacent edges have the same color. k-color r-dynamic is an edge coloring of k-colors such that each edge in neighboring E(G) is at least min {r, d(u)+d(v)−2} has a different color. The dynamic r-edge coloring is defined as a mapping of c from E(G) such that |c(N(uv))| = min{r, d(u) + d(v) − 2}, where N(uv) is the neighbor of uv and c(N(uv)) is the color used by the neighboring side of uv. The minimum value of k so that the graph G satisfies the k-coloring r-dynamic edges is called the dynamic r-edge chromatic number. 1-dynamic chromatic number is denoted by λ(G), 2-dynamic chromatic number is denoted by λd(G) and for dynamic r-chromatic number is denoted by λr(G). The graphs that used in this study are graph T Ln, T CLn and the switch operation graph shack(H2,2, v, n).