The Degree of an Edge in Union and Join of Two Fuzzy Graphs
نویسندگان
چکیده
A fuzzy graph can be obtained from two given fuzzy graphs using union and join. In this paper, we find the degree of an edge in fuzzy graphs formed by these operations in terms of the degree of edges in the given fuzzy graphs in some particular cases. 1. Introduction Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975 [4]. Though it is very young, it has been growing fast and has numerous applications in various fields. During the same time Yeh and Bang have also introduced various concepts in connectedness in fuzzy graphs [9]. Mordeson and Peng introduced the concept of operations on fuzzy graphs. Sunitha and Vijayakumar discussed about complementary of the operations of union, join, Cartesian product and composition on two fuzzy graphs [8]. The degree of a vertex in fuzzy graphs which are obtained from two given fuzzy graphs using these operations were discussed by Nagoor Gani and Radha [3]. Radha and Kumaravel introduced the concept of degree of an edge and total degree of an edge in fuzzy graphs [5]. We study about the degree of an edge in fuzzy graphs which are obtained from two given fuzzy graphs using the operations of union and join. In general, the degree of an edge in union and join of two fuzzy graphs G 1 and G 2 cannot be expressed in terms of these in G 1 and G 2. In this paper, we find the degree of an edge in union and join of two fuzzy graphs G 1 and G 2 in terms of the degree of edges of G 1 and G 2 in some particular cases. First we go through some basic concepts.
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