Fuzzy Chordal Graphs and Its Properties

Chordal graphs are those graphs which have chords for each cycle of the length > 3. For large graphs/ networks, generally, the number of chords is less in number than the required number of chords to for a chordal graph. By definition, those graphs are not chordal. The algorithms and properties of chordal graphs do not apply to such cases. Also, the strength of the chords is not measured there. This study introduces a relaxation on such number of chords for the definition of chordal graphs. The notion of a fuzzy strong chord is introduced. After that, fuzzy chordal graphs and related properties are developed. The measure of fuzzy strong chords is proposed. Also, as a generation, fuzzy k-chordal graphs are developed, and isomorphism on a fuzzy chordal graph is defined. At last, area of applications of fuzzy chordal graphs and conclusions with future directions are illustrated.