Contributions to fuzzy coloring and fuzzy labeling in fuzzy graphs

Abstract

Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory newlineand fuzzy logic. It is consider to begin in 1965 after the publication of L.A. Zadeh newlineseminal work Fuzzy sets. In 1971, Zadeh introduced the basic types of fuzzy relations. newlineThe properties of fuzzy graphs have been studied by A. Kaufman, A. Rosenfeld, R.T. newlineYeh and S.Y. Bang. Recent results can be found in a 3000 articles. This thesis consists newlineof seven chapters. newlineChapter I provides an introduction to the concepts and problems related to the newlinetopic. newlineChapter II defines the vertex coloring, edge coloring and total coloring of antifuzzy graph using and#120573;-cuts. newlineChapter III defines the vertex coloring, edge coloring and total coloring of antifuzzy graph and discusses the chromatic excellence in anti-fuzzy graph. newlineChapter IV defines the vertex coloring, edge coloring and total coloring of newlineintuitionistic-fuzzy graph and discusses the chromatic excellence in intuitionistic-fuzzy newlinegraph. newlineChapter V defines the vertex coloring, edge coloring and total coloring of newlinehesitancy- fuzzy graph and discusses the chromatic excellence in hesitancy-fuzzy graph. newlineChapter VI conferred the hesitancy-fuzzy labeling graph, hesitancy-fuzzy magic newlinelabeling graph and its properties. newlineChapter VII discusses the anti-fuzzy labeling graph, anti-fuzzy labeling tree and newlineits properties newline