### Nilai Kromatik pada Graf Hasil Operasi

#### Abstract

Let *G* = (*V* (*G*)*; E*(*G*)) be connected nontrivial graph. Edge coloring is de-¯ned as *c* : *E*(*G*) *! f*1*;* 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 min*fr; d*(*u*) + *d*(*v*) *¡* 2*g* have di®erent color. An Edge *r* dynamic is a proper *c* of *E*(*G*) such that *jc*(*N*(*uv*))*j* = min*fr; d*(*u*) + *d*(*v*) *¡* 2*g*, 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*(

*H*

_{3}

*; e; n*),

*amal*(

*Bt*

_{3}

*; v; n*) and

*amal*(

*S*

_{4}

*; v; n*).

Keywords: *r*-dynamic coloring, *r*-dynamic chromatic number, graph operations.

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