ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 10 (2021), no.3, 1227–1235 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.10.3.11 MORPHISM OF m-BIPOLAR FUZZY GRAPH Ramakrishna Mankena, T.V. Pradeep Kumar, Ch. Ramprasad 1 , and J. Vijaya Kumar ABSTRACT. In this article, weak, co-weak, isomorphism and morphism between two m-bipolar fuzzy graphs (m-BPFGs) are defined and studied their various properties. 1. I NTRODUCTION Fuzzy sets are introduced for the parameters to solve problems related to vague and uncertain in real life situations were given by Zadeh [8] in 1965. The limitations of traditional model were overcome by the introduction of bipolar fuzzy set concept in 1994 by Zhang [9]. This was further improved by Chen et al. [3] to m-polar fuzzy set theory. Free body diagrams using set of nodes connected by lines representing pairs are good problem solving tools in non-deterministic real life situations. Thus, Rosenfeld [6] first initiated the fuzzy graphs by taking fuzzy relations on fuzzy sets in 1975. Akram [1] introduced the notion of bipolar fuzzy graphs and stud- ied some isomorphic properties on it. Rashmanlou et al. [7] studied categorical properties of bipolar fuzzy graphs. Ghorai and Pal [4,5] introduced generalized m-polar fuzzy graphs and studied some isomorphic properties and density of 1 corresponding author 2020 Mathematics Subject Classification. 05C72. Key words and phrases. m-BPFG, Isomorphism, Morphism. Submitted: 16.02.2021; Accepted: 04.03.2021; Published: 16.03.2021. 1227