Pdf on jan 1, 2004, nagoor gani and others published 16. Chapter 2 fuzzy graph structures basic concepts in this chapter, we introduce the concept of fuzzy graph structures as an extension to that of graph structures of. The concept of chromatic number of fuzzy graphs was introduced by munoz6 et. Pdf in this paper, regular fuzzy graphs, total degree and totally regular fuzzy graphs are introduced. Nagoorgani and basheerahamed 18 have introduced the strong and weak domination concepts in fuzzy graphs. On irregular fuzzy graphs 519 regular fuzzy graph of total degree k or a ktotally regular fuzzy graph. Now, in this paper, some types of tfuzzy graphs an considered, fuzzy adjacency matrix of that tfuzzy graphs is obtains. On edge regular square fuzzy graphs research india publications. The total degree of a index terms fuzzy graph, direct sum, effective fuzzy graph, regular fuzzy graph, connectedness, upper and lower truncations. Coloring of fuzzy graphs plays a vital role in theory and practical applications. Nagoorgani and radha 11 defined regular fuzzy graphs. A characterization of regular fuzzy graphs on a cycle is provided. Pdf regular properties of fuzzy graphs researchgate. The regular property and connectedness of the direct sum of two fuzzy graphs are also studied.
Also r, m, kregularity on fuzzy graphs whose underlying crisp graph is a. Then we provide a necessary and sufficient condition under which they are equivalent. Generalized fuzzy graphs, effective edge, regular graphs. The total status tsg of a fuzzy graph g is the sum of all. New approach on regular fuzzy graph research india publications. In this paper, strongly regular fuzzy graph which is analogous to the concept of strongly regular graph in crisp graph theory is introduced and examples are presented, necessary and sufficient condition for a cycle to be strongly regular fuzzy graph is provided and some properties of strongly regular fuzzy graph are studied. Some properties of vertex regular fuzzy graph are studied and they are examined for. Planar graph is a special type in crisp as well as in fuzzy graphs. A necessary and sufficient condition under which they. Completeness and regularity of generalized fuzzy graphs. Antipodal intervalvalued fuzzy graphs hossein rashmanlou 1 and madhumangal pal 2.
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