I. Rosyida, Widodo, Ch R. Indrati, D. Indriati
We consider a fuzzy graph G(V; E ) with a crisp vertex set V and a fuzzy edge set E . A fuzzy graph has some -cut graphs for 2 [0; 1] which are crisp graphs. Coloring of a fuzzy graph could be transformed into classical coloring of the -cut graphs. Let G1(V1; E1) and G2(V2; E2) be two fuzzy graphs with fuzzy chromatic numbers 1(G1) = f(k; 1 (k))g and 2(G2) = f(k; 2 (k))g, respectively. Let G = G1 [ G2 be a union of G1 and G2. By coloring of the -cut graphs, we get the result that membership function of fuzzy chromatic number of the union (G) = f(k; (k))g satises a property (k) = maxf1 (k); 2 (k)g for k 2 f1; 2; 3⋯ jV1 [ V2jg: Furthermore, we also verify the connection between the fuzzy chromatic number (G) and maxf1; 2g through a defuzzication dependent at a decision level. © 2019 IOP Publishing Ltd. All rights reserved.
Department of Mathematics, Universitas Negeri Semarang, Semarang, Indonesia; Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia; Department of Mathematics, Universitas Sebelas Maret, Surakarta, Indonesia
