Chromatics Number of Operation Graphs

Abstract

Let G = (V (G); E(G)) be connected nontrivial graph. Edge coloring is de-¯ned as c : E(G) ! f1; 2; :::; kg; k 2 N, with the conditions no edges adja-cent having the same color. Coloring k-color edges r-dynamic is edges color-ing as much as k color such that every edges in E(G) with adjacent at least minfr; d(u) + d(v) ¡ 2g have di®erent color. An Edge r dynamic is a proper c of E(G) such that jc(N(uv))j = minfr; d(u) + d(v) ¡ 2g, for each edge N(uv) is the neighborhood of uv and c(N(uv)) is color used to with adjacent edges of uv. the edge r-dynamic chromatic number, written as ¸(G), is the minimum k such that G has an edge r-dynamic k-coloring. chromatic number 1-dynamic writ-ten as ¸(G), chromatic number 2-dynamic written as ¸d(G) And for chromatic number r-dynamic written as ¸(G). A graph is used in this research namely gshack(H3; e; n), amal(Bt3; v; n) and amal(S4; v; n). Keywords: r-dynamic coloring, r-dynamic chromatic number, graph operations.