Isnaini Rosyida, Widodo, Ch. Rini Indrati, Diari Indriati, Nurhaida
We focus on fuzzy graphs with crisp vertex and fuzzy edge sets. A concept of the fuzzy chromatic number of these graphs based on fuzzy independent vertex set is used in this paper. A modified algorithm called a fuzzy chromatic algorithm is developed to find the fuzzy chromatic number of union of fuzzy graphs. Running time and complexity of the algorithm are also analyzed. Furthermore, we investigate some properties of the fuzzy chromatic number of union of fuzzy graphs. Finally, an application of the fuzzy chromatic number to determine the number of phases of an integrated traffic light system is proposed. We get different phases with different degrees of safety. © 2019 Elsevier B.V.
Department of Mathematics, Universitas Negeri Semarang, Semarang, Indonesia; Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia; Department of Mathematics, Universitas Sebelas Maret, Surakarta, Indonesia; Department of Mathematics, Universitas Papua, Papua, Indonesia
