Affiliations: [a] Department of Computer Science, University College of Adib, Sari, Iran
| [b]
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India
| [c]
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
| [d]
Department of Physics, Sari Branch, Islamic Azad University, Sari, Iran
| [e]
Department of Industrial & Management Engineering, Hanyang University, Erica Campus, Ansan, South Korea
Correspondence:
[*]
Corresponding author: Biswajit Sarkar, Department of Industrial & Management Engineering, Hanyang University, Erica Campus, Ansan, South Korea. E-mail: [email protected].
Abstract: Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they have many applications in networks. In this paper, at first we define three new operations on interval-valued fuzzy graphs namely strong product, tensor product and lexicographic product. Likewise, we study about the degree of a vertex in interval-valued fuzzy graphs which are obtained from two given interval-valued fuzzy graphs using the operations Cartesian product, composition, tensor and strong product of two interval-valued fuzzy graphs. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large interval-valued fuzzy graph as a combination of small, interval-valued fuzzy graphs and to derive its properties from those of the smaller ones.
