On intuitionistic product fuzzy graphs article pdf available in italian journal of pure and applied mathematics 3838. A graph is a pair v, r, where v is a set and r is a relation on v. Several authors introduced and studied what they called product fuzzy graphs, see for example 41. Pdf different types of product of fuzzy graphs researchgate. Also we defined the strong product of two fuzzy graphs and studied its properties 8.
Index terms fuzzy graph, direct sum, strong product, effective fuzzy graph, connectedness, upper and lower truncations. First let us recall some preliminary definitions that can be found in 19. We have illustrated that these operations are not commutative and studied. Pdf corona product of two fuzzy graphs which is analogous to the concept corona product operation in crisp graph theory is defined. Fuzzy graphs introduced by rosenfeld in 197512,9,10. Shovandogra 11 introduced different types of products of fuzzy graphs. It is proved that when two fuzzy graphs are effective then their strong product is always effective and it is proved that the strong product of two complete fuzzy graphs is complete. Different types of product of fuzzy graphs international journal of. On product fuzzy graphs annals of fuzzy mathematics and. Pdf domination in product fuzzy graphs mahioub shubatah. In addition, sahoo and pal 20 discussed the concept of the intuitionistic fuzzy competition graph. Pdf on strong product of two fuzzy graphs ijsrp journal academia. In this paper, we study about the degree of a vertex in fuzzy graphs which are obtained from two given fuzzy graphs using the operations.
Pdf in this paper, beta product and gamma product of two fuzzy graphs are introduced and we proved that the beta product of two regular fuzzy graphs. Pdf n this paper, we provide three new operations on intuitionistic product fuzzy graphs. Pdf on jan 1, 2016, talal alhawary and others published on product fuzzy graphs find, read and cite all the research you need on researchgate. Abstract in this paper, the strong product of two fuzzy graphs is defined. On complement of intuitionstic product fuzzy graphs. Certain types of product bipolar fuzzy graphs springerlink. Pdf new fuzzy graphs can be obtained from two given fuzzy graphs using different types of fuzzy graph product. In this paper, we provide three new products on product fuzzy graphs, we give su cient conditions for each one of them to be strong and we show that if any of these products is complete, then at least one factor is strong. It is proved that when two fuzzy graphs are effective then their strong product is always effective and. The operations of union, join, cartesian product and composition on two fuzzy graphs were defined by moderson. The elements of v are thought of as vertices of the graph and the elements of r are thought of as the edges similarly, any fuzzy relation.
In this paper, we have introduced the concept of lexicographic products of two fuzzy graphs namely, lexicographic minproduct and lexicographic maxproduct which are analogous to the concept lexicographic product in crisp graph theory. Revised revised 30 january 2016 accepted 2 march 2016 abstract. The notion of product fuzzy graph has generalized for intuitionistic product fuzzy graph and definition of complement and ring sum of two intuitionistic. Different types of products on intuitionistic fuzzy graphs core.
In this paper, at first the concepts of regular and totally regular product bipolar fuzzy graphs is introduced. Then necessary and sufficient conditions are established under which regular and totally regular product bipolar fuzzy graph becomes equivalent. In this paper, the strong product of two fuzzy graphs is defined. On product fuzzy graphs talal alhawary, bayan horani received 16 january 2016. Product fuzzy graphs ijcsns international journal of computer. Alhawary 32 introduced the concept of balanced fuzzy graphs. Every product fuzzy graph is a fuzzy graph, but the converse need not be true.