Fuzzy Eulerian and Fuzzy Hamiltonian Graphs with Their Applications
Abdul. Muneera1, T. Nageswara Rao2, R.V.N. Srinivasa Rao3
1Abdul. Muneera , Scholar, Koneru Lakshmaiah Education Foundation , Vaddeswaram, Guntur, Andhra Pradesh, India and Lecturer, Department of Mathematics , Andhra Loyola Institute of Engineering and Technology, Vijayawada, Andhra Pradesh, India.
2T. Nageswara Rao, Dept of Mathematics , Koneru Lakshmaiah Education Foundation , Vaddeswaram, Guntur, Andhra Pradesh, India.
3R.V. N. Srinivas Rao, Department of Mathematics, Wollega University Ethopia.

Manuscript received on November 20, 2019. | Revised Manuscript received on November 28, 2019. | Manuscript published on 30 November, 2019. | PP: 7995-7999 | Volume-8 Issue-4, November 2019. | Retrieval Number: D4386118419/2019©BEIESP | DOI: 10.35940/ijrte.D4386.118419

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Abstract: In this article we discussed prominence of Fuzzy Eulerian and Fuzzy Hamiltonian graphs. Fuzzy logic is introduced to study the uncertainty of the event. In Fuzzy set theory we assign a membership value to each element of the set which ranges from 0 to 1. The earnest efforts of the researchers are perceivable in the relevant establishment of the subject integrating coherent practicality and reality. Fuzzy graphs found an escalating number of applications in day to day life system where the information intrinsic in the system varies with different levels of accuracy. In this article we initiated the model of fuzzy Euler graphs (FEG) and also fuzzy Hamiltonian graphs (FHG). We explored about fuzzy walk, fuzzy path, fuzzy bridge, fuzzy cut node, fuzzy tree, fuzzy blocks, fuzzy Eulerian circuit and fuzzy Hamiltonian cycle. Here we studied some applications of Fuzzy Eulerian graphs and fuzzy Hamiltonian graphs in real life.
Keywords: Fuzzy Walk, Fuzzy Path, Fuzzy Bridge, Fuzzy Block, Fuzzy Euler Graph, Fuzzy Eulerian Circuit, Fuzzy Hamiltonian Cycle.
Scope of the Article: Fuzzy Logics.