Analisa Pewarnaan Total r-Dinamis pada Graf Lintasan dan Graf Hasil Operasi

Abstract

Graph coloring began to be developed into coloring dynamic. One of the developments of dynamic coloring is r-dynamic total coloring. Suppose G = (V (G), E(G)) is a non-trivial connected graph. Total coloring is defined as c : (V (G) ∪ E(G)) → 1, 2, ..., k, k ∈ N, with condition two adjacent vertices and the edge that is adjacent to the vertex must have a different color. r-dynamic total coloring defined as the mapping of the function c from the set of vertices and edges (V (G) ∪ E(G)) such that for every vertex v ∈ V (G) satisfy |c(N(v))| = min[r, d(v) + |N(v)|], and for each edge e = uv ∈ E(G) satisfy |c(N(e))| = min[r, d(u) + d(v)]. The minimal k of color is called r-dynamic total chromatic number denoted by χ 00(G). The 1-dynamic total chromatic number is denoted by χ 00(G), chromatic number 2-dynamic denoted with χ 00 d (G) and r-dynamic chromatic number denoted by χ 00 r (G). The graph that used in this research are path graph, shackle of book graph (shack(B2, v, n) and generalized shackle of graph friendship gshack(F4, e, n).