Analisa Pewarnaan Total r-Dinamis pada Graf Lintasan dan Graf Hasil Operasi - Desi Febriani Putri; Dafik Dafik; Kusbudiono Kusbudiono (jcgant, 2021)
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^′′(G). The 1-dynamic total chromatic number is denoted by χ^′′(G), chromatic number 2-dynamic denoted with χ^′′_d(G) and r-dynamic chromatic number denoted by χ^′′_r(G). The graph that used in this research are path graph, shackle of book graph (shack(B_2,v,n) and generalized shackle of graph friendship gshack(F_4,e,n).